If $f (x) = {(a - x^{n})}^{1 / n}$ , where a > 0 and n &epsis; N, show that f (f (x)) = x.

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Solution

$(f o f) (x) = f (f (x)) = f ({(a - x^{n})}^{\frac{1}{n}}) = {[a - {({(a - x^{n})}^{\frac{1}{n}})}^{n}]}^{\frac{1}{n}} = {[a - (a - x^{n})]}^{\frac{1}{n}} = {(x^{n})}^{\frac{1}{n}} = x$

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