Question

What is the inverse of the following function? 50 points

Answer 1

The inverse of the given function $f(x)=\sqrt[5]{x^3}$ is $f^{-1}(x)=x^{\frac{5}{3}}$

Inverse of a function

The given function is:

$f(x)=\sqrt[5]{x^3}$

This function can be written in exponent form as:

$f(x)=x^\frac{3}{5}$

Make x the subject of the formula:

$x=[f(x)]^\frac{5}{3}$

Let x be replaced by $f^{-1}(x)$ and f(x) be replaced by x

The inverse function therefore becomes:

$f^{-1}(x)=x^{\frac{5}{3}}\\\\ f^{-1}(x)=\sqrt[3]{5}$

Learn more on the inverse of a function here:brainly.com/question/3831584

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