Home
Class 12
MATHS
Let f: X -> Ybe an invertible function....

Let `f: X -> Y`be an invertible function. Show that the inverse of `f^(-1)`is f, i.e., `(f^(-1))^(-1)= f`.

A

`[pi/4,(5pi)/4] rarr [sqrt(2),3sqrt(2)]`

B

`[-pi/4,(3pi)/4] rarr [sqrt(2),3sqrt(2)]`

C

`[-(3pi)/4,(3pi)/4] rarr [sqrt(2),-3sqrt(2)]`

D

`[-(3pi)/4,-pi/4] rarr [sqrt(2),3sqrt(2)]`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f : X rarr Y be an invertible function . Show that the inverse of f^(-1) is f . i.e., (f^(-1))^(-1)= f .

Let f :X rarr Y be an invertible function . Show that f has unique inverse . (Hint : Suppose g_(1) and g_(2) are two inverse of f. Then for all y inY,(fog_1)(y) =I_(Y) (y) = (fog_(2))(y). Use one - one ness of f).

Consider f: R ^+ to [4 ,oo] given by f(x) =x^2 + 4 show that f is f invertible with the inverse f^(-1) of given by f^(-1) (y) = sqrt(y-4) where R^+ is set of all non - negative real numbers .

Consider f: R ^+ to [4 ,oo] given by f(x) =x^2 + 4 show that f is f invertible with the inverse f^(-1) of given by f^(-1) (y) = sqrt(y-4) where R^+ is set of all non - negative real numbers .

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f is a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx, f(0) = (4-e^(2))/(3) , find f(x).

Let f(x) be linear functions with the properties that f(1) le f(2), f(3) ge f(4) " and " f(5)=5. Which one of the following statements is true?

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then g''f(x) is equal to

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g^(prime)(f(x)) equal. (a) f^(prime)(c) (b) 1/(f^(prime)(c)) (c) f(c) (d) none of these

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these