So the steps to find the inverse are:
- Change f(x) to y
- Switch the positions of x and y
- Solve for y
- Change y to f^-1(x)
[tex] f(x)=-2+ \frac{2}{3}x\\\\y=-2+ \frac{2}{3}x\\\\x=-2+ \frac{2}{3}y [/tex]
Now let's solve for y as such:
[tex] x=-2+ \frac{2}{3}y \\\\x+2=\frac{2}{3}y\\\\\frac{3}{2} (x+2)=y\\\\\frac{3}{2}x+3=y\\\\\frac{3}{2}x+3=f^{-1}(x) [/tex]
Your inverse is f^-1(x) = 3/2x + 3
