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

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

1 Answer

  • 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 $f:R\to R$ given by $f(x)=(3-x^3)^{1/3}$
We know that $(fof)(x)=f(f(x))$
$\Rightarrow fof =f((3-x^3)^{1/3})$ $=[3-((3-x^3)^{1/3})^3]^{1/3}$
$\Rightarrow fof =[3-(3-x^3)]^{1/3}$ $=(x^3)^{1/3}=x$
Therefore $(fof)(x)= (C)\; x$ is the correct answer.
answered Feb 26, 2013 by meena.p
edited Mar 19, 2013 by balaji.thirumalai

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