Question

If $f\left(x\right)={(1-x^3)}^{\frac{1}{3}}$, then find $fof\left(x\right)$

• A. $\frac{1}{x}$
• B. $x$
• C. $x^2$
• D. $x^3$

Answer 1

The correct option is B $x$

Given, $f\left(x\right)={(1-x^3)}^{\frac{1}{3}}$
Therefore, $fof\left(x\right)=f\left[f\left(x\right)\right]$
$=f\left({(1-x^3)}^{\frac{1}{3}}\right)={[1-{\left\{{(1-x^3)}^{\frac{1}{3}}\right\}}^3]}^{\frac{1}{3}}$
$={[1-{(1-x)}^3]}^{\frac{1}{3}}={\left(x^3\right)}^{\frac{1}{3}}=x$