Question

Find the inverse of the function. Is the inverse a function? Simplify your answer.y=2x-6

Answer 1

To find the inverse of the function, refer to the given function then replace all x with y, and y with x.

Given y = 2x - 6

Swap the variables x and y

`y=2x-6\Longrightarrow x=2y-6`

Then solve such that y is on the left side, with a coefficient of 1.

`\begin{gathered} x=2y-6 \\ x-x-2y=2y-2y-x-6 \\ \cancel{x-x}-2y=\cancel{2y-2y}-x-6 \\ -2y=-x-6 \\ \\ \text{Divide both sides by }-2\text{ to get rid of the coefficient of }y\text{ on the left side} \\ \frac{\cancel{-2}y}{\cancel{-2}}=(-x-6)/(-2) \\ y=(-x)/(-2)+(-6)/(-2) \\ y=(x)/(2)+3 \end{gathered}`

Therefore, the inverse of the function y = 2x - 6 is y = x/2 + 3.