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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let f:$R\rightarrow R$ be the functions defined by $f(x)=x^3+5.$ Then $f^{-1}(x)$ is

\begin{array}{1 1}(A)\;(x+5)^{\frac{1}{3}} & (B)\;(x-5)^{\frac{1}{3}}\\(C)\;(5-x)^{\frac{1}{3}} & (D)\;5-x\end{array}

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  • A function g is inverse of $f:R \to R $ if $fog=gof=I_R\;ie \;g=f^{-1}$
$f:R \to R$
Let $y=x^3+5 \qquad y \to R$
we define a function $g(y)=(y-5)^{1/3}$
Also $fog(g)=f(g(y))$
'B' option is correct



answered Mar 5, 2013 by meena.p

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