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  4. If f(x) = (a - xn)1/n, then f(f(x)) =

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Q. If $f(x) = (a - x^n)^{1/n}$, then $f(f(x)) =$

Relations and Functions - Part 2

Solution:

$f(x)=(a-x^n)^{1/n}=y$
$\therefore \,f(y)=(a-y^n)^{1/n}=\left[a-[(a-x^n)^{\frac{1}{n}}]^n\right]^{\frac{1}{n}}$
$=[a-(a-x^n)]^{\frac{1}{n}}=(x^n)^{1/n}=x$