English

What is the Range of the Function `F (X) = ([X - 1])/(X -1) ?`

Advertisements
Advertisements

Question

What is the range of the function

`f (x) = ([x - 1])/(x -1) ?`

Advertisements

Solution

` f (x) = ([x - 1])/(x - 1) = (+(x-1)) /(x-1)` = ±1

Range of f = {-1 ,1 }

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Functions - Exercise 2.5 [Page 74]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.5 | Q 33 | Page 74

RELATED QUESTIONS

Show that the function f in `A=R-{2/3} ` defined as `f(x)=(4x+3)/(6x-4)` is one-one and onto hence find f-1


Let f : R → R be defined as f(x) = x4. Choose the correct answer.


Find the number of all onto functions from the set {1, 2, 3, ..., n} to itself.


Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x2


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = sinx


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.


Show that if f1 and f2 are one-one maps from R to R, then the product f1 × f2 : R → R defined by (f1 × f2) (x) = f1 (x) f2 (x) need not be one - one.


If f(x) = 2x + 5 and g(x) = x2 + 1 be two real functions, then describe each of the following functions:
(1) fog
(2) gof
(3) fof
(4) f2
Also, show that fof ≠ f2


State with reason whether the following functions have inverse :

g : {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}


Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1


If f : Q → Qg : Q → Q are two functions defined by f(x) = 2 x and g(x) = x + 2, show that f and g are bijective maps. Verify that (gof)−1 = f−1 og −1.


Let f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.


Which of the following graphs represents a one-one function?


Let f  be a function from C (set of all complex numbers) to itself given by f(x) = x3. Write f−1 (−1).


Let f : R → Rg : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 − x2. Write fog (−2).


If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).


Let M be the set of all 2 × 2 matrices with entries from the set R of real numbers. Then, the function f : M→ R defined by f(A) = |A| for every A ∈ M, is

 


The range of the function

\[f\left( x \right) =^{7 - x} P_{x - 3}\]

 


Let f be an injective map with domain {xyz} and range {1, 2, 3}, such that exactly one of the following statements is correct and the remaining are false.

\[f\left( x \right) = 1, f\left( y \right) \neq 1, f\left( z \right) \neq 2 .\]

The value of

\[f^{- 1} \left( 1 \right)\] is 

 


Let

\[f : R \to R\]  be a function defined by

\[f\left( x \right) = \frac{e^{|x|} - e^{- x}}{e^x + e^{- x}} . \text{Then},\]
 

If the function

\[f : R \to R\]  be such that

\[f\left( x \right) = x - \left[ x \right]\] where [x] denotes the greatest integer less than or equal to x, then \[f^{- 1} \left( x \right)\]

 


 Let
\[g\left( x \right) = 1 + x - \left[ x \right] \text{and} f\left( x \right) = \begin{cases}- 1, & x < 0 \\ 0, & x = 0, \\ 1, & x > 0\end{cases}\] where [x] denotes the greatest integer less than or equal to x. Then for all \[x, f \left( g \left( x \right) \right)\] is equal to


Let A = ℝ − {3}, B = ℝ − {1}. Let f : A → B be defined by \[f\left( x \right) = \frac{x - 2}{x - 3}, \forall x \in A\] Show that f is bijective. Also, find
(i) x, if f−1(x) = 4
(ii) f−1(7)


Write about strcmp() function.


Let R be the set of real numbers and f: R → R be the function defined by f(x) = 4x + 5. Show that f is invertible and find f–1.


The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______


Let A be a finite set. Then, each injective function from A into itself is not surjective.


Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

k(x) = x2 


The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.


The function f : R → R defined by f(x) = 3 – 4x is ____________.


The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.


Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given information, f is best defined as:


An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

  • Ravi wants to know among those relations, how many functions can be formed from B to G?

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • The function f: R → R defined by f(x) = x − 4 is ____________.

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.

Answer the following questions using the above information.

  • Let f: R → R be defined by f(x) = x2 is:

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.

Answer the following questions using the above information.

  • Let : N → R be defined by f(x) = x2. Range of the function among the following is ____________.

Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is ______.


If A = {x ∈ R: |x – 2| > 1}, B = `{x ∈ R : sqrt(x^2 - 3) > 1}`, C = {x ∈ R : |x – 4| ≥ 2} and Z is the set of all integers, then the number of subsets of the set (A ∩ B ∩ C) C ∩ Z is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×