Answer:
[tex]g^{-1}(x) =(\frac{x}{10})^{5} +2[/tex]
Step-by-step explanation:
So we have the function [tex]g(x)=10\sqrt[5]{x-2}[/tex]. To find the inverse, we first set the function equal to y:
[tex]y=10\sqrt[5]{x-2}[/tex]
Then, we switch all the y and x variables, like this:
[tex]x=10\sqrt[5]{y-2}[/tex]
Now, we solve for y to find the inverse function:
[tex]x=10\sqrt[5]{y-2}[/tex]
[tex]\frac{x}{10} =\sqrt[5]{y-2}[/tex]
[tex](\frac{x}{10})^{5} =y-2[/tex]
[tex](\frac{x}{10})^{5} +2=y[/tex]
[tex]y=(\frac{x}{10})^{5} +2[/tex]
[tex]g^{-1}(x) =(\frac{x}{10})^{5} +2[/tex]
