If f(x)=a−xn1/n,a>0,n∈N, then f(f(x))=

If $f (x) = {(a - x^{n})}^{1 / n}, a > 0, n \in N$ , then $f (f (x)) =$

A
1
B
n
C
x
D
nx

Solution:

We have $f (x) = {(a - x^{n})}^{\frac{1}{n}}$

$\Rightarrow f (f (x)) = {(a - (f (x))^{n})}^{\frac{1}{n}} = {(a - (a - x^{n}))}^{1 / n} = {(x^{n})}^{\frac{1}{n}} = x$ .

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