Change f(x) to a y and switch places with y and x as below.
[tex]x= \frac{2}{3} y-6[/tex]
Solve the equation for y
[tex]x + 6 = \frac{2}{3} y[/tex]
Multiply each term by the reciprocal of [tex] \frac{2}{3} [/tex]
[tex] \frac{3}{2} (x+6) = y[/tex]
Distribute
[tex] \frac{3}{2} x+9=y[/tex]
Change y to [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)= \frac{3}{2} x+9[/tex]
