Question

What is the inverse of f(x)-x/x+2, where x ≠ -2

Answer 1

Explanation:

You can take the inverse of a function by replacing all x-values in the equation with y-values and vice versa and subsequently solving for y:

Equation given:

`f(x) = (-x)/(x+2)`

Replace all x-values with y and all y-values with x:

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

Solve for y:

`x(y+2) = -y\\\\xy + 2x = -y\\\\2x = -y - xy\\\\2x = y(-1+-x)\\\\-(2x)/(x+1) =y`

This is the inverse of f(x), where x ≠ 2..