Question

If f(x) = (a – xⁿ)^1/n, where a > 0 and n is a positive integer, then f(f(x)) = x Is it true?

Answer 1

Given f(x) = (a – xⁿ)^1/n 

 f(f(x)) = f(a – xⁿ)^1/n 

= f(b), b = (a – xⁿ)^1/n 

= (a – bⁿ)^1/n = (a – {(a – aⁿ)^1/n}ⁿ)^1/n 

= (a – (a – xⁿ))^1/n

= (xⁿ)^1/n 

= x 

So, it is true