Online Mock Tests
Chapters
Chapter 2: Relations
Chapter 3: Functions
Chapter 4: Measurement of Angles
Chapter 5: Trigonometric Functions
Chapter 6: Graphs of Trigonometric Functions
Chapter 7: Values of Trigonometric function at sum or difference of angles
Chapter 8: Transformation formulae
Chapter 9: Values of Trigonometric function at multiples and submultiples of an angle
Chapter 10: Sine and cosine formulae and their applications
Chapter 11: Trigonometric equations
Chapter 12: Mathematical Induction
Chapter 13: Complex Numbers
Chapter 14: Quadratic Equations
Chapter 15: Linear Inequations
Chapter 16: Permutations
Chapter 17: Combinations
Chapter 18: Binomial Theorem
Chapter 19: Arithmetic Progression
Chapter 20: Geometric Progression
Chapter 21: Some special series
Chapter 22: Brief review of cartesian system of rectangular co-ordinates
Chapter 23: The straight lines
Chapter 24: The circle
Chapter 25: Parabola
Chapter 26: Ellipse
Chapter 27: Hyperbola
Chapter 28: Introduction to three dimensional coordinate geometry
Chapter 29: Limits
Chapter 30: Derivatives
Chapter 31: Mathematical reasoning
Chapter 32: Statistics
Chapter 33: Probability

Chapter 3: Functions
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 3 Functions Exercise 3.1 [Pages 7 - 8]
Define a function as a set of ordered pairs.
Define a function as a correspondence between two sets.
What is the fundamental difference between a relation and a function? Is every relation a function?
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(a) range of f, i.e. f(A).
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(b) pre-images of 6, −3 and 5.
find: f(1), f(−1), f(0) and f(2).
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(b) {x : f(x) = −2}
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(c) whether f(xy) = f(x) : f(y) holds
Write the following relations as sets of ordered pairs and find which of them are functions:
(a) {(x, y) : y = 3x, x ∈ {1, 2, 3}, y ∈ [3,6, 9, 12]}
Write the following relations as sets of ordered pairs and find which of them are functions:
(b) {(x, y) : y > x + 1, x = 1, 2 and y = 2, 4, 6}
Write the following relations as sets of ordered pairs and find which of them are functions:
{(x, y) : x + y = 3, x, y, ∈ [0, 1, 2, 3]}
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
f, g, h are three function defined from R to R as follow:
(ii) g(x) = sin x
Find the range of function.
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(b) f2 = {(1, 1), (2, 7), (3, 5)}
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?
(a) R1 = [(p, 1), (q, 2), (r, 1), (s, 2)]
(b) R2 = [(p, 1), (q, 1), (r, 1), (s, 1)]
(c) R3 = [(p, 1), (q, 2), (p, 2), (s, 3)
(d) R4 = [(p, 2), (q, 3), (r, 2), (s, 2)].
Let A = [9, 10, 11, 12, 13] and let f : A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
The function f is defined by \[f\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 3 \\ 3x, & 3 \leq x \leq 10\end{cases}\] The relation g is defined by \[g\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 2 \\ 3x, & 2 \leq x \leq 10\end{cases}\]
Show that f is a function and g is not a function.
If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]
Express the function f : X → R given by f(x) = x3 + 1 as set of ordered pairs, where X = {−1, 0, 3, 9, 7}
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 3 Functions Exercise 3.2 [Pages 11 - 12]
If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
If f(x) = (x − a)2 (x − b)2, find f(a + b).
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
If \[f\left( x \right) = \begin{cases}x^2 , & \text{ when } x < 0 \\ x, & \text{ when } 0 \leq x < 1 \\ \frac{1}{x}, & \text{ when } x \geq 1\end{cases}\]
find: (a) f(1/2), (b) f(−2), (c) f(1), (d)
If \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
If \[f\left( x \right) = \frac{x - 1}{x + 1}\] , then show that
(i) \[f\left( \frac{1}{x} \right) = - f\left( x \right)\]
(ii) \[f\left( - \frac{1}{x} \right) = - \frac{1}{f\left( x \right)}\]
If f(x) = (a − xn)1/n, a > 0 and n ∈ N, then prove that f(f(x)) = x for all x.
If for non-zero x, af(x) + bf \[\left( \frac{1}{x} \right) = \frac{1}{x} - 5\] , where a ≠ b, then find f(x).
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 3 Functions Exercise 3.3 [Page 18]
Find the domain of the real valued function of real variable:
(i) \[f\left( x \right) = \frac{1}{x}\]
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{x - 7}\]
Find the domain of the real valued function of real variable:
(iii) \[f\left( x \right) = \frac{3x - 2}{x + 1}\]
Find the domain of the real valued function of real variable:
(iv) \[f\left( x \right) = \frac{2x + 1}{x^2 - 9}\]
Find the domain of the real valued function of real variable:
(v) \[f\left( x \right) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}\]
Find the domain of the real valued function of real variable:
(i) \[f\left( x \right) = \sqrt{x - 2}\]
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]
Find the domain of the real valued function of real variable:
(iii) \[f\left( x \right) = \sqrt{9 - x^2}\]
Find the domain of the real valued function of real variable:
(iv) \[f\left( x \right) = \frac{\sqrt{x - 2}}{3 - x}\]
Find the domain and range of the real valued function:
(i) \[f\left( x \right) = \frac{ax + b}{bx - a}\]
Find the domain and range of the real valued function:
(ii) \[f\left( x \right) = \frac{ax - b}{cx - d}\]
Find the domain and range of the real valued function:
(iii) \[f\left( x \right) = \sqrt{x - 1}\]
Find the domain and range of the real valued function:
(iv) \[f\left( x \right) = \sqrt{x - 3}\]
Find the domain and range of the real valued function:
(v) \[f\left( x \right) = \frac{x - 2}{2 - x}\]
Find the domain and range of the real valued function:
(vi) \[f\left( x \right) = \left| x - 1 \right|\]
Find the domain and range of the real valued function:
(vii) \[f\left( x \right) = - \left| x \right|\]
Find the domain and range of the real valued function:
(viii) \[f\left( x \right) = \sqrt{9 - x^2}\]
Find the domain and range of the real valued function:
(ix) \[f\left( x \right) = \frac{1}{\sqrt{16 - x^2}}\]
Find the domain and range of the real valued function:
(x) \[f\left( x \right) = \sqrt{x^2 - 16}\]
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 3 Functions Exercise 3.4 [Page 38]
Find f + g, f − g, cf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{ and } \frac{f}{g}\] in :
(a) If f(x) = x3 + 1 and g(x) = x + 1
Find f + g, f − g, cf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{ and } \frac{f}{g}\] in :
(b) If \[f\left( x \right) = \sqrt{x - 1}\] and \[g\left( x \right) = \sqrt{x + 1}\]
Let f(x) = 2x + 5 and g(x) = x2 + x. Describe (i) f + g (ii) f − g (iii) fg (iv) f/g. Find the domain in each case.
If f(x) be defined on [−2, 2] and is given by \[f\left( x \right) = \begin{cases}- 1, & - 2 \leq x \leq 0 \\ x - 1, & 0 < x \leq 2\end{cases}\] and g(x)
\[= f\left( \left| x \right| \right) + \left| f\left( x \right) \right|\] , find g(x).
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(i) f + g
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(ii) g − f
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(iii) f g
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(iv) \[\frac{f}{g}\]
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(v) \[\frac{g}{f}\]
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(vi) \[2f - \sqrt{5} g\]
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(vii) f2 + 7f
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(viii) \[\frac{5}{8}\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(ii) fg
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iii) \[\frac{f}{g}\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),
If f, g and h are real functions defined by
The function f is defined by
Let f, g : R → R be defined, respectively by f(x) = x + 1 and g(x) = 2x − 3. Find f + g, f − g and \[\frac{f}{g}\] .
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
Let f(x) = x2 and g(x) = 2x+ 1 be two real functions. Find (f + g) (x), (f − g) (x), (fg) (x) and \[\left( \frac{f}{g} \right) \left( x \right)\] .
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 3 Functions Exercise 3.5 [Pages 41 - 42]
Write the range of the real function f(x) = |x|.
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
If f(x) = cos [π2]x + cos [−π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).
Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
Write the range of the function f(x) = ex−[x], x ∈ R.
Let \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] . Then write the value of α satisfying f(f(x)) = x for all x ≠ −1.
If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
If f(x) = 4x − x2, x ∈ R, then write the value of f(a + 1) −f(a − 1).
If f, g, h are real functions given by f(x) = x2, g(x) = tan x and h(x) = loge x, then write the value of (hogof)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
Write the domain and range of function f(x) given by
Write the domain and range of \[f\left( x \right) = \sqrt{x - \left[ x \right]}\] .
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.
Let f and g be two functions given by
f = {(2, 4), (5, 6), (8, −1), (10, −3)} and g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, −5)}.
Find the domain of f + g
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, −4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}
Find the domain of fg.
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 3 Functions [Pages 42 - 45]
Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
(a) {(1, 2), (1, 3), (2, 3), (3, 3)}
(b) [(1, 3), (2, 4)]
(c) {(1, 3), (2, 2), (3, 3)}
(d) {(1, 2), (2, 3), (3, 2), (3, 4)}
If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
(a) 3
(b) −3
(c) {−3, 3}
(d) ϕ
Which one of the following is not a function?
(a) {(x, y) : x, y ∈ R, x2 = y}
(b) {(x, y) : x, y ∈, R, y2 = x}
(c) {(x, y) : x, y ∈ R, x2 = y3}
(d) {(x, y) : x, y ∈, R, y = x3}
If f(x) = cos (log x), then the value of f(x2) f(y2) −
(a) −2
(b) −1
(c) 1/2
(d) None of these
If f(x) = cos (log x), then the value of f(x) f(y) −\[\frac{1}{2}\left\{ f\left( \frac{x}{y} \right) + f\left( xy \right) \right\}\] is
(a) −1
(b) 1/2
(c) −2
(d) None of these
Let f(x) = |x − 1|. Then,
(a) f(x2) = [f(x)]2
(b) f(x + y) = f(x) f(y)
(c) f(|x| = |f(x)|
(d) None of these
The range of f(x) = cos [x], for π/2 < x < π/2 is
(a) {−1, 1, 0}
(b) {cos 1, cos 2, 1}
(c) {cos 1, −cos 1, 1}
(d) [−1, 1]
Which of the following are functions?
(a) {(x, y) : y2 = x, x, y ∈ R}
(b) {(x, y) : y = |x|, x, y ∈ R}
(c) {(x, y) : x2 + y2 = 1, x, y ∈ R}
(d) {(x, y) : x2 − y2 = 1, x, y ∈ R}
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and} g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to
(a) f(3x)
(b) {f(x)}3
(c) 3f(x)
(d) −f(x)
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
(a) 12
(b) 8
(c) 6
(d) 3
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\] is equal to
(a) {f(x)}2
(b) {f(x)}3
(c) 2f(x)
(d) 3f(x)
If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is
(a) 1
(b) −1
(c) 0
(d) ±1
If \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
(a) \[\frac{1}{2}\left[ f\left( 2x \right) + f\left( 2y \right) \right]\]
(b) \[\frac{1}{2}\left[ f\left( 2x \right) - f\left( 2y \right) \right]\]
(c) \[\frac{1}{4}\left[ f\left( 2x \right) + f\left( 2y \right) \right]\]
(d) \[\frac{1}{4}\left[ f\left( 2x \right) - f\left( 2y \right) \right]\]
If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to
(a) \[- \frac{7}{4}\]
(b) \[\frac{5}{2}\]
(c) −1
(d) None of these
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
(a) 2x
(b) 2|x|
(c) −2x
(d) −2|x|
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
(a) R
(b) R − {1}
(c) R − {−1/2, 1}
(d) None of these
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
(a) 1
(b) 2
(c) 3
(d) 4
If f(x) = cos (loge x), then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right) - \frac{1}{2}\left\{ f\left( xy \right) + f\left( \frac{x}{y} \right) \right\}\] is equal to
(a) cos (x − y)
(b) log (cos (x − y))
(c) 1
(d) cos (x + y)
(e) 0
Let f(x) = x, \[g\left( x \right) = \frac{1}{x}\] and h(x) = f(x) g(x). Then, h(x) = 1
(a) x ∈ R
(b) x ∈ Q
(c) x ∈ R − Q
(d) x ∈ R, x ≠ 0
If \[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] for x ∈ R, then f (2002) =
(a) 1
(b) 2
(c) 3
(d) 4
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
(a) [3/4, 1)
(b) (3/4, 1]
(c) [3/4, 1]
(d) (3/4, 1)
Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (is
(a) [1, −1]
(b) [x : 0 ≤ x ≤ 4]
(c) {1}
(d) {x : −4 ≤ x ≤ 0}
(e)
{-1,1}
If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are
(a) 1, 2
(b) −1, 2
(c) −1, −2
(d) 1, −2
If f : [−2, 2] → R is defined by \[f\left( x \right) = \begin{cases}- 1, & \text{ for } - 2 \leq x \leq 0 \\ x - 1, & \text{ for } 0 \leq x \leq 2\end{cases}\] , then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =
(a) {−1}
(b) {0}
(c) \[\left\{ - \frac{1}{2} \right\}\]
(d) ϕ
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
(a) 0.5
(b) 0.6
(c) 0.7
(d) 0.8
f is a real valued function given by \[f\left( x \right) = 27 x^3 + \frac{1}{x^3}\] and α, β are roots of \[3x + \frac{1}{x} = 12\] . Then,
(a) f(α) ≠ f(β)
(b) f(α) = 10
(c) f(β) = −10
(d) None of these
If \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,
(a) f(α) = f(β) = −9
(b) f(α) = f(β) = 63
(c) f(α) ≠ f(β)
(d) none of these
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(x) =
(a) \[\frac{1}{14}\left( \frac{3}{x} + 5x - 6 \right)\]
(b) \[\frac{1}{14}\left( - \frac{3}{x} + 5x - 6 \right)\]
(c) \[\frac{1}{14}\left( - \frac{3}{x} + 5x + 6 \right)\]
(d) None of these
If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\] x ∈ R, then
(a) f(x) = f(1 − x)
(b) f(x) + f(1 − x) = 0
(c) f(x) + f(1 − x) = 1
(d) f(x) + f(x − 1) = 1
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
(a) f(π/2) = 1
(b) f(π) = 2
(c) f(π/4) = −1
(d) None of these
The domain of the function
(a) \[\left[ - \sqrt{3}, \sqrt{3} \right]\]
(b) \[\left[ - 1 - \sqrt{3}, - 1 + \sqrt{3} \right]\]
(c) [−2, 2]
(d) \[\left[ - 2 - \sqrt{3}, - 2 + \sqrt{3} \right]\]
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
(a) (−∞, −3] ∪ (2, 5)
(b) (−∞, −3) ∪ (2, 5)
(c) (−∞, −3) ∪ [2, 5]
(d) None of these
The domain of the function \[f\left( x \right) = \sqrt{\frac{\left( x + 1 \right) \left( x - 3 \right)}{x - 2}}\] is
(a) [−1, 2) ∪ [3, ∞)
(b) (−1, 2) ∪ [3, ∞)
(c) [−1, 2] ∪ [3, ∞)
(d) None of these
The domain of definition of the function \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is
(a) [1, ∞)
(b) (−∞, 3)
(c) (1, 3)
(d) [1, 3]
The domain of definition of the function \[f\left( x \right) = \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{1 - x}{1 + x}}\] is
(a) (−∞, −2] ∪ [2, ∞)
(b) [−1, 1]
(c) ϕ
(d) None of these
The domain of definition of the function f(x) = log |x| is
(a) R
(b) (−∞, 0)
(c) (0, ∞)
(d) R − {0}
The domain of definition of \[f\left( x \right) = \sqrt{4x - x^2}\] is
(a) R − [0, 4]
(b) R − (0, 4)
(c) (0, 4)
(d) [0, 4]
The domain of definition of \[f\left( x \right) = \sqrt{x - 3 - 2\sqrt{x - 4}} - \sqrt{x - 3 + 2\sqrt{x - 4}}\] is
(a) [4, ∞)
(b) (−∞, 4]
(c) (4, ∞)
(d) (−∞, 4)
The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is
(a) (−3, − 2) ∪ (2, 3)
(b) [−3, − 2) ∪ [2, 3)
(c) [−3, − 2] ∪ [2, 3]
(d) None of these
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
(a) R − {0}
(b) R − {−1, 1}
(c) {−1, 1}
(d) None of these
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
(a) {−1, 1}
(b) {−1, 0, 1}
(c) {1}
(d) (0, ∞)
The range of the function f(x) = |x − 1| is
(a) (−∞, 0)
(b) [0, ∞)
(c) (0, ∞)
(d) R
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
(a) \[f\left( xy \right) = f\left( x \right)f\left( y \right)\]
(b) \[f\left( xy \right) \geq f\left( x \right)f\left( y \right)\]
(c) \[f\left( xy \right) \leq f\left( x \right)f\left( y \right)\]
(d) none of these
If \[\left[ x \right]^2 - 5\left[ x \right] + 6 = 0\], where [.] denotes the greatest integer function, then
(a) x ∈ [3, 4]
(b) x ∈ (2, 3]
(c) x ∈ [2, 3]
(d) x ∈ [2, 4)
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
(a) [1/3, 1]
(b) [−1, 1/3]
(c) (−∞, −1) ∪ [1/3, ∞)
(d) [−1/3, 1]
Chapter 3: Functions

RD Sharma solutions for Class 11 Mathematics Textbook chapter 3 - Functions
RD Sharma solutions for Class 11 Mathematics Textbook chapter 3 (Functions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Class 11 Mathematics Textbook chapter 3 Functions are Cartesian Product of Sets, Brief Review of Cartesian System of Rectanglar Co-ordinates, Relation, Concept of Functions, Some Functions and Their Graphs, Algebra of Real Functions, Ordered Pairs, Equality of Ordered Pairs, Pictorial Diagrams, Graph of Function, Pictorial Representation of a Function, Exponential Function, Logarithmic Functions.
Using RD Sharma Class 11 solutions Functions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.
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