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# question on functions

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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