Let `f: X -> 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 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