Question

Find inverse of f(x) = 2 + 3x / x - 2

Know answer is 2x + 2 / x - 3 I just want someone to explain the steps for my revision!

Thank you.

Answer 1

Okay so, we switch out f(x) with y - I’m sure you know this and we get y=2+3x/x-2.

Now just interchange x and y -> x=2+3y/y-2, now multiply both sides with (y-2), we get (y-2)x=2+3y.

Multiply x with the brackets, getting xy-2x=2+3y. Move 3y to the left changing it’s sign, also for -2x to the right: xy-3y=2+2x.

Factor out y from (xy-3y) and get (3-x)y=2+2x - now divide both sides by (3-x) resulting in y=2+2x/3-x .