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

Let f:X to Y be an invertible function. Show that f has uniques inverse.

If f: R to R is an invertible functions such that f(x) and f^(-1) (x) are symmetric about the line y = -x , then

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

If f: R to R is defined by f(x) =x-[x] , then the inverse function f^(-1)(x) =

Let f : (-1, 1) to R be a differentiable function with f(0) = -1 and f'(0) = 1 . Let g(x) = [f(2f(x) + 2)]^2 . Then g'(0) is equal to

If g is the inverse function of f and f^1(x) = sin x then g^1(x) is

Let f (x ) be a polynomial function of second degree. If f (1) = f( -1) and a,b,c are in A.P., then f' (a), f'(c ) are in