The inverse of the given function [tex]f(x)=\sqrt[5]{x^3}[/tex] is [tex]f^{-1}(x)=x^{\frac{5}{3}}[/tex]
Inverse of a function
The given function is:
[tex]f(x)=\sqrt[5]{x^3}[/tex]
This function can be written in exponent form as:
[tex]f(x)=x^\frac{3}{5}[/tex]
Make x the subject of the formula:
[tex]x=[f(x)]^\frac{5}{3}[/tex]
Let x be replaced by [tex]f^{-1}(x)[/tex] and f(x) be replaced by x
The inverse function therefore becomes:
[tex]f^{-1}(x)=x^{\frac{5}{3}}\\\\ f^{-1}(x)=\sqrt[3]{5}[/tex]
Learn more on the inverse of a function here:https://brainly.com/question/3831584
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