Question

How do you find the inverse of `f(x) =(4-x)/(3x)`?

Answer 1

Let `y = f(x)` and solve for `x` to find:

`f^-1(y) = 4/(3y+1)`

Explanation:

Let `y = f(x) = (4-x)/(3x)`

Then `3y = (4-x)/x = 4/x - x/x = 4/x-1`

So `3y+1 = 4/x`

So `x = 4/(3y+1)`

So `f^-1(y) = 4/(3y+1)`