If $f: R \rightarrow R$ be given by $f(x)=\left(3-x^{3}\right)^{\frac{1}{3}},$ then $fof(x)$ is ..........
If $f: R \rightarrow R$ be given by $f(x)=\left(3-x^{3}\right)^{\frac{1}{3}},$ then $fof(x)$ is ..........
$f : R \rightarrow R$ be given as $f ( x )=\left(3-x^{3}\right)^{\frac{1}{3}}$
$\therefore fof ( x )= f ( f ( x ))=f\left(3-x^{3}\right)^{\frac{1}{3}}$ $=\left[3-\left(\left(3-x^{3}\right)^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{3}}$
$=\left[3-\left(3-x^{3}\right)\right]^{\frac{1}{3}}=\left(x^{3}\right)^{\frac{1}{3}}$
$\therefore fof(x)=x$
The correct answer is $D$.
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