If `f(x) = 2^x`, prove that `f(x+3) - f(x-1) = (15)/2 f(x)`.

If f(x) =x+1/x , prove that : [f(x)]^3 = f(x^3)+3f (1/x) .

If f (x) = (a-x^n)^(1//n) prove that f(f(x)) = x

If f (x) = sqrtx , prove that : (f(x+h)-f(x))/h=1/(sqrt(x+h)+ sqrtx) .

For the function f, f(x)=x^2-6x + 8 , prove that f’(5)-3 f'(2)= f’(8).

If ‘f’ is a real function defined by : f(x)= (x-1)/(x+1) , then prove that f (2x) = (3 f(x)+1)/(f(x)+3) .

If y= f(x)=(2x+3)/(5x-2) , prove that f(y)=x.

If y= f(x) =(3x-1)/(5x-3) , prove that f(y) =x.

If f(x) =2x-3 , then f^(-1)(x) =

If f(x) = x^2+5x+2 , then f'(3) is

If f(x) = log_e ((1+x)/(1-x)) , prove that f((2x)/(1+x^2))=2f(x) .