Answer
The answer is $f^{-1}(x)=\frac{x^{5}-2}{4}\\$
Work Step by Step
$\ The\ given\ function\ is\ f(x)=\sqrt[5]{4x+2}\\
\ This\ can\ be\ rewritten\ as\ y=\sqrt[5]{4x+2}\\
\ Taking\ the\ fifth\ power\ on\ both\ sides\ we\ get\ ,\\
y^{5}=4x+2\\
\ Subtracting\ 2\ on\ both\ sides\ we\ get\ ,\\
4x=y^{5}-2\\
\ Dividing\ on\ both\ sides\ by\ 4\ we\ get\ ,\\
x=\frac{y^{5}-2}{4}\\
\ So\ we\ get\ f^{-1}(x)=\frac{x^{5}-2}{4}\\$
