If f: R → R be given by f(x)=left(3-x^{3}right)^{frac{1}{3}}, then fof(x) is ..........

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1.Relation and Function

medium

If $f: R \rightarrow R$ be given by $f(x)=\left(3-x^{3}\right)^{\frac{1}{3}},$ then $fof(x)$ is ..........

$x^{\frac{1}{3}}$

$x^{3}$

$\left(3-x^{3}\right)$

$x$

Solution

$f : R \rightarrow R$ 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 $D$.

Standard 12

Mathematics

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