The inverse of the function is given by option C.
[tex]\rm q^{-1}x = (\dfrac{x}{10})^5 +2[/tex]
What is an Inverse Function?
An inverse function of a function is found by exchanging the y with x and vice versa and then the equation is solved for y.
The function [tex]\rm q(x) = 10\sqrt[5]{x-2}[/tex]
let q(x) = y
[tex]\rm y = 10\sqrt[5]{x-2}[/tex]
Now x and y are interchanged
[tex]\rm x = 10\sqrt[5]{y-2}\\\\\dfrac{x}{10} = \sqrt[5]{y-2}\\\\\\y-2 = (\dfrac{x}{10})^5\\\\y = (\dfrac{x}{10})^5 +2\\\\\\q^{-1}x = (\dfrac{x}{10})^5 +2[/tex]
Therefore, the inverse of the function is given by option C.
To know more about Inverse Function
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