Finding Inverses of Equations
Pg. 58-59
February 13, 2015
Warm-Up (Left Side)
• How did we find the graph of the inverse of a
function?
• What line is the inverse reflected across?
Title (Right Side)
• Finding Inverses Algebraically
Essential Question
• How do I find the inverse of an equation using
algebraic steps?
To find the inverse of an equation:
1. Exchange the x’s with y’s (rewrite the
equation)
2. Resolve the equation for the y-variable
3. Write your inverse equation using f-1(x) or y-1
Remember the notation for an inverse uses
f-1(x) or y-1 to signify that it is an inverse.
Example 1
Given f(x)=3x – 6, find the inverse…
f(x)=y so the original equation is y=3x-6
1. Rewrite exchanging the x’s and y’s: x=3y – 6
2. Resolve for the y-variable: add 6… x + 6 = 3y
divide by 3: 1/3 x + 2 = y
3. Rewrite the equation using the inverse
notation:
f-1(x) = 1/3 x + 2
Example 2
Given g(x) = 2/3 x + 5
1. Rewrite:
x = 2/3 y + 5
2. Subtract 5:
x – 5 = 2/3 y
Multiply by 3/2 (reciprocal): 3/2 x – 15/2 = y
3. Write the inverse:
g-1(x) = 3/2 x – 15/2
(or g-1(x) = 1.5x – 7.5)
Assignment: Find the inverse equations for the
following. Show all work on your own paper.
1. y = 3x + 5
2. f(x) = ¼ x
3. g(x) = 2/5 x – 5
4. h(x) = -3/4 x – 9
5. y = -2x + 8
6. f(x) = 17x – 51
7. g(x) = 5x - 25
Reflection
• If the original graph is a linear function, what
kind of graph will the inverse be?