Question

If $f\left(x\right)=(a-x^n{)}^{\frac{1}{n}}$ then $fof\left(x\right)$ is?

Answer 1

$f\left(x\right)={(a-x^n)}^{\frac{1}{n}}f\left(f\left(x\right)\right)=f\left({(a-x^n)}^{\frac{1}{n}}\right)={(a-{\left({(a-x^n)}^{\frac{1}{n}}\right)}^n)}^{\frac{1}{n}}={(a-(a-x^n))}^{\frac{1}{n}}={(a-a+x^n)}^{\frac{1}{n}}={\left(x^n\right)}^{\frac{1}{n}}=x\therefore f\left(f\left(x\right)\right)=x$