4.7 Inverse Linear Functions
ALGEBRA 1
Content Standards
A.CED.2 Create equations in two or more
variables to represent relationships between
quantities; graph equations on coordinate axes
with labels and scales.
F.BF.4a Solve an equation of the form f (x ) = c
for a simple function f that has an inverse and
write an expression for the inverse.
Mathematical Practices
6 Attend to precision.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State
School Officers. All rights reserved.
You represented relations as tables, graphs,
and mappings.
• Find the inverse of a relation.
• Find the inverse of a linear function.
Inverse Relations
Example 1
A. Find the inverse of each relation.
{(−3, 26), (2, 11), (6, −1), (−1, 20)}
You Try!
B. Find the inverse of each relation .
Example 2
A. Graph the inverse of each relation.
Find some points that cross nicely
on the graph!
Flip the x and y values of those
points, then graph!
You Try!
B. Graph the inverse of each relation.
Finding Inverse Equations
Follow these steps…
1) Replace f(x) with y!
2) Flip x and y
3) Solve for y
4) Change y back to f-1(x)
Example 3
A. Find the inverse of the function f (x) = –3x + 27.
Step 1:
Step 2:
Step 3:
Step 4:
Example 4
You Try!
Example 5
SALES Carter sells paper supplies and makes a
base salary of $2200 each month. He also earns 5%
commission on his total sales. His total earnings
f(x) for a month in which he compiled x dollars in
total sales is f(x) = 2200 + 0.05x.
A. Find the inverse function.
Example 5B
SALES Carter sells paper supplies and makes a
base salary of $2200 each month. He also earns 5%
commission on his total sales. His total earnings
f(x) for a month in which he compiled x dollars in
total sales is f(x) = 2200 + 0.05x.
B. What do x and f –1(x)represent in the context of
the inverse function?
Example 5C
SALES Carter sells paper supplies and makes a
base salary of $2200 each month. He also earns 5%
commission on his total sales. His total earnings
f(x) for a month in which he compiled x dollars in
total sales is f(x) = 2200 + 0.05x.
C. Find Carter’s total sales for last month if his
earnings for that month were $3450.
End of the Lesson
 Mini Practice Activity
 Homework: On the back of your notes sheet!