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Consider 2 functions $f(x)$, $g(x)$ that is defined on the interval $[0, \infty)$ where
\[f(x)=x^3+x^2+x+2\]
\[g(x)=2f^{-1}(x)-1\]
Find the value of $g^{-1}(0)+g^{-1}(3)$.

 Jan 26, 2021
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Consider 2 functions \(f(x), g(x)\)that is defined on the interval \([0, \infty)\) where
\(f(x)=x^3+x^2+x+2\)
\(g(x)=2f^{-1}(x)-1\)
Find the value of \(g^{-1}(0)+g^{-1}(3)\).

 

Hello Guest!

 

\(g(x)=\dfrac{2}{x^3+x^2+x+2}-1\)

 

\(g^{-1}(x)=\dfrac{1}{\dfrac{2}{x^3+x^2+x+2}-1}\)

 

\(g^{-1}(0)=\dfrac{1}{\dfrac{2}{0^3+0^2+0+2}-1}=\frac{1}{0}=\infty\)

 

\(g^{-1}(3)=\dfrac{1}{\dfrac{2}{3^3+3^2+3+2}-1}=-1.\overline{051282}\)

 

 

\(g^{-1}(0)+g^{-1}(3)=\infty\)

 Jan 26, 2021
edited by asinus  Jan 26, 2021

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