Question

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

• A. $x$
• B. $x^n$
• C. $p^{1/n}$
• D. $p-x^n$

Answer 1

The correct option is A $x$

Given, $f\left(x\right)=(p-x^n{)}^{\frac{1}{n}}$

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

$=(p-(p-x^n){)}^{\frac{1}{n}}$

$=(x^n{)}^{\frac{1}{n}}$

$=x$