Question

Let f(x)=2/3x-6 what is the inverse function?

Answer 1

Change f(x) to a y and switch places with y and x as below.
$x= \frac{2}{3} y-6$

Solve the equation for y
$x + 6 = \frac{2}{3} y$

Multiply each term by the reciprocal of $\frac{2}{3}$
$\frac{3}{2} (x+6) = y$

Distribute
$\frac{3}{2} x+9=y$

Change y to $f^{-1}(x)$
$f^{-1}(x)= \frac{3}{2} x+9$