Question

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

Answer 1

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:

$f(x) = \frac{-x}{x+2}$

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

$x = \frac{-y}{y+2}$

Solve for y:

$x(y+2) = -y\\\\xy + 2x = -y\\\\2x = -y - xy\\\\2x = y(-1+-x)\\\\-\frac{2x}{x+1} =y$

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