Advertisements
Advertisements
प्रश्न
If f : R → R is defined by f(x) = x2, write f−1 (25)
Advertisements
उत्तर
Let f−1 (25) =x ... (1)
⇒ f (x) = 25
⇒ x2 = 25
⇒ x2 − 25 = 0
⇒ (x−5) (x+5) = 0
⇒ x = ±5
⇒ f−1 (25) = {−5, 5} [from (1)]
APPEARS IN
संबंधित प्रश्न
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by f(x) = `((x - 2)/(x - 3))`. Is f one-one and onto? Justify your answer.
Let S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.
F = {(a, 2), (b, 1), (c, 1)}
Prove that the function f : N → N, defined by f(x) = x2 + x + 1, is one-one but not onto
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = sinx
Show that the exponential function f : R → R, given by f(x) = ex, is one-one but not onto. What happens if the co-domain is replaced by`R0^+` (set of all positive real numbers)?
Give examples of two functions f : N → N and g : N → N, such that gof is onto but f is not onto.
If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?
Let f be any real function and let g be a function given by g(x) = 2x. Prove that gof = f + f.
if f (x) = `sqrt (x +3) and g (x) = x ^2 + 1` be two real functions, then find fog and gof.
State with reason whether the following functions have inverse:
h : {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}
Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1
Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {a, b, c}.
Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x3. Write f−1(1).
If f : R → R is defined by f(x) = x2, find f−1 (−25).
Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\] be a function defined by f(x) = cos [x]. Write range (f).
If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).
Let f : R → R, g : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 − x2. Write fog (−2).
Let\[A = \left\{ x \in R : - 1 \leq x \leq 1 \right\} = \text{B and C} = \left\{ x \in R : x \geq 0 \right\} and\]\[S = \left\{ \left( x, y \right) \in A \times B : x^2 + y^2 = 1 \right\} \text{and } S_0 = \left\{ \left( x, y \right) \in A \times C : x^2 + y^2 = 1 \right\}\]
Then,
\[f : R \to R \text{given by} f\left( x \right) = x + \sqrt{x^2} \text{ is }\]
The function \[f : [0, \infty ) \to \text {R given by } f\left( x \right) = \frac{x}{x + 1} is\]
The range of the function
\[f\left( x \right) =^{7 - x} P_{x - 3}\]
The function
\[f : R \to R\] defined by\[f\left( x \right) = \left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)\]
(a) one-one but not onto
(b) onto but not one-one
(c) both one and onto
(d) neither one-one nor onto
If \[f\left( x \right) = \sin^2 x\] and the composite function \[g\left( f\left( x \right) \right) = \left| \sin x \right|\] then g(x) is equal to
Let C be the set of complex numbers. Prove that the mapping f: C → R given by f(z) = |z|, ∀ z ∈ C, is neither one-one nor onto.
The number of bijective functions from set A to itself when A contains 106 elements is ____________.
A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}
- Mr. ’X’ and his wife ‘W’ both exercised their voting right in the general election-2019, Which of the following is true?
Let f: R → R defined by f(x) = 3x. Choose the correct answer
'If 'f' is a linear function satisfying f[x + f(x)] = x + f(x), then f(5) can be equal to:
Consider a function f: `[0, pi/2] ->` R, given by f(x) = sinx and `g[0, pi/2] ->` R given by g(x) = cosx then f and g are
The solution set of the inequation log1/3(x2 + x + 1) + 1 > 0 is ______.
Let f(x) be a polynomial function of degree 6 such that `d/dx (f(x))` = (x – 1)3 (x – 3)2, then
Assertion (A): f(x) has a minimum at x = 1.
Reason (R): When `d/dx (f(x)) < 0, ∀ x ∈ (a - h, a)` and `d/dx (f(x)) > 0, ∀ x ∈ (a, a + h)`; where 'h' is an infinitesimally small positive quantity, then f(x) has a minimum at x = a, provided f(x) is continuous at x = a.
Which one of the following graphs is a function of x?
![]() |
![]() |
| Graph A | Graph B |
A function is called into if:
A function is called bijective if it is both:
If every seat in a classroom is occupied by one student, the situation resembles:


