Given:
[tex]y=tan(5x)[/tex]
To find:
The inverse for the function.
Explanation:
Let us swap the variables, we get
[tex]x=tan(5y)[/tex]
Solve for y we get,
[tex]\begin{gathered} tan^{-1}(x)=5y \\ \frac{\tan^{-1}(x)}{5}=y \\ y=\frac{\tan^{-1}(x)}{5} \end{gathered}[/tex]
Therefore, the inverse for the function is,
[tex]\frac{\tan^{-1}(x)}{5}[/tex]
Final answer:
The inverse for the function is,
[tex]\frac{\tan^{-1}(x)}{5}[/tex]
