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# If f : R → R be given by f (x) = (3 − x) to the power 3 the whole power 1 over 3, then fof (x) is A x to the power 1 over 3 B x to the power 3 C x D 3 - x to the power 3

Q.  13 If $f : R \rightarrow R$ be given by $f(x) = (3 - x^3)^{\frac{1}{3}}$, then $fof(x)$ is

(A) $x^{\frac{1}{3}}$

(B) $x^3$

(C) $x$

(D) $(3 - x^3)$

Views

$f(x) = (3 - x^3)^{\frac{1}{3}}$

$fof(x)$$=f(f(x))=f((3-x^{3})^{\frac{1}{3}})$

$=[3- ((3-x^{3})^{\frac{1}{3}})^{3}]^{\frac{1}{3}}$

$=([3- ((3-x^{3})]^{\frac{1}{3}})$

$= (x^{3})^{\frac{1}{3}}$

$=x$

Thus,$fof(x)$ is x.

Hence, option c is correct answer.

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