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  4. Let f: R → R be the function defined by f(x) = x3 + 5. Then f-1(x) is

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Q. Let $f$ : $R \to R$ be the function defined by $f(x) = x^3 + 5$. Then $f^{-1}(x)$ is

Relations and Functions - Part 2

Solution:

$f \left(x\right)=x^{3}+5$
$\Rightarrow y=x^{3}=5$
$\Rightarrow x^{3}=y-5$
$\Rightarrow x=\left(y-5\right)^{1/3}$
$\therefore f ^{-1}\left(x\right)=\left(x-5\right)^{1/3}$