Question

If $f\left(x\right)=(a{x}^n{)}^{1/n},$ where $n\in N$, then $f\left\{f\right(x\left)\right\}$ equals

• A. $0$
• B. $x$
• C. $x^n$
• D. none of these

Answer 1

The correct option is D none of these

We have, $f\left(x\right)=(a{x}^n{)}^{1/n}=a^{1/n}x=kx$ where $k=a^{1/n}$

$\therefore f\left\{f\right(x\left)\right\}=kf\left(x\right)=k^{2}x=a^{2/n}x$