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.

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 defined as f(x) = (2x-7)/( 4) is an invertible function, write f^(-1) (x) .

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

f : R to R be defined as f(x) = 4x + 5 AA x in R show that f is invertible and find f^(-1) .

f: Z to Z is a linear function defined by f={(1,1),(0,-1),(2,3)} , find f(x)

Let f(x) be a polynomial function such that f(x). f(1/x) = f(x) + f(1/x). If f(4) = 65, then f^(')(x) =

Let R+ be the set of all non-negative real number. Show that the faction f : R, to [4, oo) defined f(x) = x^(2) + 4 is invertible. Also write the inverse of f.

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