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Questions  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Q)

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


$(A)\; x^{\frac{1}{3}}$
$(B)\; x^3$
$(C)\; x$
$(D)\; (3-x^3)$

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A)
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  • Given two functions $f : A \to B $ and $ g: B \to C,$ then composition of $f $ and $g, gof : A \to C$ by $gof(x) = g(f(x))$ for all $x \in A$. Therefore it follows that $fof = f(f(x)).$
Given a function $f : R \to R$ be given by $f(x) = (3-x^3)^{\frac{1}{3}}$
we know that $(fof)(x) = f(f(x))$
$\implies fof = f((3 - x^3)^{1/3}) = [3 - ((3-x^3)^{1/3})^3]^{1/3}$
$\implies fof = [3 - (3-x^3)]^{1/3} = (x^3)^{1/3} = x$
$\therefore (fof)(x) = (C)x$ is the correct answer.
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