Question

Let $f:R\to R$ given by $f\left(x\right)={(3-x^3)}^{1/3}$. Then $fof\left(x\right)$ is

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

Answer 1

The correct option is A $x$

$fof\left(x\right)=f\left(f\right(x\left)\right)\Rightarrow fof\left(x\right)=f\left({(3-x^3)}^{1/3}\right)=f\left(y\right)$
Where $y={(3-x^3)}^{1/3}$
$\Rightarrow f\left(y\right)={\{3-(3-x^3)\}}^{1/3}\Rightarrow f\left(y\right)={\left(x^3\right)}^{1/3}=x\therefore fof\left(x\right)=x$