Question

what’s the inverse of
f(x) = -2 + 2/3x

Answer 1

So the steps to find the inverse are:

1. Change f(x) to y
2. Switch the positions of x and y
3. Solve for y
4. Change y to f^-1(x)

$f(x)=-2+ \frac{2}{3}x\\\\y=-2+ \frac{2}{3}x\\\\x=-2+ \frac{2}{3}y$

Now let's solve for y as such:

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

Your inverse is f^-1(x) = 3/2x + 3