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Q.
Let $f : R \rightarrow R , g : R \rightarrow R$ be two functions such that $f(x)=2 x-3, g(x)=x^{3}+5$. The function $(\text { fog })^{-1}(x)$ is equal to
Relations and Functions - Part 2
Solution:
We have, $f(x)=2 x-3, g(x)=x^{3}+5$
$($ fog $) x=f\left(x^{3}+5\right)$
$=2\left(x^{3}+5\right)-3=2 x^{3}+7$
Let $y=($ fog $) x=2 x^{3}+7$
$\Rightarrow x=\left(\frac{y-7}{2}\right)^{1 / 3} $
$\Rightarrow (\text { fog })^{-1} x=\left(\frac{x-7}{2}\right)^{1 / 3}$