Question

Determine the inverse of the function by interchanging the variables and solving for y in terms of X

Answer 1

$\begin{gathered} \\ \text{Given y=}\frac{x}{2}-\frac{3}{2} \end{gathered}$

We are required to find the inverse of the function

The first step is to interchange the variable x for y

$x=\frac{y}{2}-\frac{3}{2}$

The next step is to make y the subject of the formula

$\begin{gathered} x=\frac{y}{2}-\frac{3}{2} \\ \frac{y}{2}=x+\frac{3}{2} \\ \text{ Multiply the equation throughout by 2} \\ y\text{ = 2x + 3} \end{gathered}$

The answer is y = 2x + 3