Question

How can I find the inverse function of Y=3x+2? My friend and I have different answers and we don't know who's right or wrong. I got what's in the picture.

Answer 1

The inverse of this function is y = $\frac{x - 2}{3}$

In order to find the inverse of any function, you must start by switching the y and x terms. After doing so, you can then solve for your new y. The result will be the inverse function. The work for this one is done below for you.

y = 3x + 2----> switch the x and y

x = 3y + 2 ----> subtract 2

x - 2 = 3y ----> divide by 3

$\frac{x - 2}{3}$ = y ----> switch the order for consistency

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

This is now your inverse function.

Answer 2

$y=3x+2\\ 3x=y-2\\ x=\dfrac{y-2}{3}\\\\ y^{-1}=\dfrac{x-2}{3}$