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Question Number 118960 by bramlexs22 last updated on 21/Oct/20

$$Givenf:R\to Randg:R\to R$$$$wheref\left(x\right)=x^3+3andg\left(x\right)=2x+1.Find$$$$thevalueof{f}^{-1}\left(g^{-1}\left(23\right)\right).$$

Answered by benjo_mathlover last updated on 21/Oct/20

$$let{f}^{-1}\left(g^{-1}\left(23\right)\right)=q$$$$then{g}^{-1}\left(23\right)=f\left(q\right)org\left(f\left(q\right)\right)=23$$$$g(q^3+3)=23\Rightarrow 2(q^3+3)+1=23$$$$2q^3+7=23,q=\sqrt[3]{8}=2.$$$$Hence{f}^{-1}\left(g^{-1}\left(23\right)\right)=2$$

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