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+ (2)/(3)x\\\\y=-2+ (2)/(3)x\\\\x=-2+ (2)/(3)y`

Now let's solve for y as such:

`x=-2+ (2)/(3)y \\\\x+2=(2)/(3)y\\\\(3)/(2) (x+2)=y\\\\(3)/(2)x+3=y\\\\(3)/(2)x+3=f^(-1)(x)`

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