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

If f (x) = log_e ((1+x)/(1-x)) , prove that: f (x) +f (y)= f ((x+y)/(1+xy)) .

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

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

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

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

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

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

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 f(x) = (x-1)/(x+1) , x ne -1 then show that f(f(x)) =(-1)/x

If f(x)=(a-x^(n))^(1//n),"where a "gt 0" and "n in N , then fof (x) is equal to