$f: R \rightarrow R ; g: R \rightarrow R$ are two functions such that $\mathrm{f}(x)=2 x-3, \mathrm{~g}(x)=x^3+5$, then $(f \circ g)^{-1}(-9)$ is

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Aicharya · Accepted Answer

We have, $\mathrm{f}(x)=2 x-3, \mathrm{~g}(x)=x^3+5$ $\begin{aligned} \operatorname{fog}(x) & =\mathrm{f}(\mathrm{g}(x)) \ & =2 \mathrm{~g}(x)-3 \ & =2\left(x^3+5ight)-3=2 x^3+7 \end{aligned}$ Let $(f \circ g)(x)=y=2 x^3+7$ $\begin{aligned} & y=2 x^3+7 \ & \Rightarrow y-7=2 x^3 \ & \Rightarrow x^3=\frac{y-7}{2} \ & \Rightarrow x=\left(\frac{y-7}{2}ight)^{\frac{1}{3}} \ 	herefore \quad & (	ext { fog })^{-1}(y)=\left(\frac{y-7}{2}ight)^{\frac{1}{3}} \ 	herefore \quad & (	ext { fog })^{-1}(-9)=\left(\frac{-9-7}{2}ight)^{\frac{1}{3}}=(-8)^{\frac{1}{3}}=-2 \end{aligned}$

$f: R \rightarrow R ; g: R \rightarrow R$ are two functions such that $\mathrm{f}(x)=2 x-3,…

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