Inverse Function
We are given the function
[tex]f(x)=4x^{\frac{2}{5}}[/tex]
To find the inverse function of f, we follow the procedure:
* Make y=f(x)
[tex]y=4x^{\frac{2}{5}}[/tex]
* Solve for x. Take the 5th power
[tex]\begin{gathered} y^5=(4x^{\frac{2}{5}})^5 \\ \text{Operating:} \\ y^5=4^5x^2 \\ \text{Dividing by }4^5\colon \\ (\frac{y}{4})^5=x^2 \\ \text{Taking the square root:} \\ x=\sqrt[\square]{(\frac{y}{4})^5}=(\frac{y}{4})^{\frac{5}{2}} \end{gathered}[/tex]
* Swapping the letters:
[tex]y=(\frac{x}{4})^{\frac{5}{2}}[/tex]
Third choice
