Step-by-step 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:
[tex]f(x) = \frac{-x}{x+2}[/tex]
Replace all x-values with y and all y-values with x:
[tex]x = \frac{-y}{y+2}[/tex]
Solve for y:
[tex]x(y+2) = -y\\\\xy + 2x = -y\\\\2x = -y - xy\\\\2x = y(-1+-x)\\\\-\frac{2x}{x+1} =y[/tex]
This is the inverse of f(x), where x ≠ 2..
