If `f(x) = 2^x`, prove that `(f(x+3))/(f(x-1))=f(4)`.

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

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

If f(x) = (1)/(1-x) , show that f(f(x)) = x

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

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

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

If f(x) = alpha x^n , prove that alpha= (f'(1))/n .

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

Prove that: int_a^b(f(x))/(f(x)+f(a+b-x))dx=(b-a)/2

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) .