Question

If $f\left(x\right)={(a-x^n)}^{1/n}$ where $a>0$ and } $n$ is a positive integer then$\left(fof\right)\left(x\right)$ is

• A. $f\left(x\right)$
• B. x
• C. 0
• D. 1

Answer 1

The correct option is B x

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

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

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

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

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

$\therefore f\left(f\right(x\left)\right)=(x^n{)}^{1/n}$

$\therefore \left(f\right(x\left)\right)=x$