If f : R$\to$ R be given by $f(x) = {(3 - {x^3})^{1/3}}$, then fof (x) is

(A) ${x^{1/3}}$

(B) ${x^3}$

(C) x

(D) $(3 - {x^3})$ .

Option C is correct

$f:R \to R$ and $f(x) = {(3 - {x^3})^{1/3}}$

$\Rightarrow$ $f[f(x)] = {[3 - {\{ f(x)\} ^3}]^{1/3}}$

$\Rightarrow$ $f[f(x)] = {[3 - {\{ {(3 - {x^3})^{1/3}}\} ^3}]^{1/3}}$

$= {[3 - (3 - {x^3})]^{1/3}} = {(3 - 3 + {x^3})^{1/3}} = x$