If f(x) =

Given:

f(x) = (a − xn)1/n, a > 0

Now,

f{ f (x)} = f (a − xn)1/n

$=\left[a-\left\{\left(a-x^{n}\right)^{1 / m}\right\}^{n}\right]^{1 / n}$

$=\left[a-\left(a-x^{n}\right)\right]^{1 / n}$

$\left.=\left[a-a+x^{n}\right)\right]^{1 / n}=\left(x^{n}\right)^{1 / n}=x^{(n \times 1 / n)}=x$

Thus, f(f(x)) = x.

Hence proved.