If $f : R → R$ be given by $f(x)=\left(3-x^3\right)^{\frac{1}{3}}$, then $fof(x)$ is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $x$
$f(x)=\left(3-x^3\right)^{\frac{1}{3}}$
$fof(x)=f(f(x))=\left(3-\left(\left(3-x^3\right)^{\frac{1}{3}}\right)^3\right)^{\frac{1}{3}}$
$=\left((3-3+x^3)\right)^{\frac{1}{3}}=(x^3)^{\frac{1}{3}}=x$