If f : R R be given by f ( x ) = ( 3 - x 3 ) 1 3 , then f ? f ( x ) is:

Question

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

Smart Achievers · Accepted Answer

(3)

Ans. $x$

Explanation:

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

$f \circ f (x) = f [f (x)]$

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

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

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

$= x$

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