Question

If $f\left(x\right)={(a-x^n)}^{1/n}$, where $a>0$ and $n\in N$, then $fof\left(x\right)$ is equal to:

• A. $a$
• B. $x$
• C. $x^n$
• D. $a^n$

Answer 1

The correct option is B

$x$

Explanation for the correct option.

Find the value of $fof\left(x\right)$:

It is given that $f\left(x\right)={(a-x^n)}^{1/n}$.

$\begin{array}{rcl}fof\left(x\right)& =& f\left[f\left(x\right)\right]\\ & =& f\left[{(a-x^n)}^{1/n}\right]\\ & =& {\left[a-{\left\{{(a-x^n)}^{1/n}\right\}}^n\right]}^{1/n}\\ & =& {\left[a-(a-x^n)\right]}^{1/n}\\ & =& {\left[a-a+x^n\right]}^{1/n}\\ & =& {\left[x^n\right]}^{1/n}\\ & =& x\end{array}$

Hence, option B is correct.