find the equation of the inverse y=3x +2

Question

find the equation of the inverse   y=3x +2

Answer 1

All answers are correct. Just one thing to add. If you have one function (let say f(x) = 3x+2) and you need to find its inverse function g(x) you can start with the composition property: f(g(x)) =x, which means

                                                               f(g) = 3g +2 = x

Then you can solve for d and find g = (x-2)/3 or g = (1/3)x -2/3 (in the slope-intercept form). The equation            f(g(x)) = x means that two functions, f(x) and g(x) are symmetric with respect to the line

y = x (it works like a bisector). You will see it if you plot both graphs on the same coordinate plane.

             

Answer 2

Sweet! So inverses sound pretty intense when you first look at them, but in reality its pretty simple

The first step to finding your inverse is to switch your x and y

original: y=3x+2 --> x=3y+2

Now that we have a new equation, we solve for y

We want the y by itself so we subtract by 2: 3y=x-2

now we divide by 3: y= (x-2)/3

if your teacher wants it in equation (y=mx+b) form you simply rewrite it:

y= x/3 -2/3 which is the same as y= 1/3 x - 2/3  (where the slope is 1/3, just in case you wanted to know :))

 

Hope this helped Dale!

Answer 3

Let's solve function y = 3x + 2 for "x" ----> 3x = y - 2 ----> x = (y - 2)/3
let's simply "switch" places for "y" and "x" and we will get inverse function for the given one
         y = (1/3)x - 2/3