Answer :
In order to find the inverse of the given function, proceed as follow:
let x as y and y as x in the given equation:
[tex]x=\frac{2}{3}y-5[/tex]Solve for y the previous equation:
[tex]\begin{gathered} x=\frac{2}{3}y-5 \\ x+5=\frac{2}{3}y \\ \frac{3}{2}(x+5)=y \\ y=\frac{3}{2}(x+5) \end{gathered}[/tex]The previous result for y is the inverse function of the original equation:
[tex]f^-(x)=\frac{3}{2}(x+5)[/tex]