Name: ____________________________________
PreCalculus Notes Chapter 1 – Functions and Their Graphs
Date:___________________
1.6 Inverse Functions
EX1. FINDING INVERSE FUNCTIONS INFORMALLY
Find the inverse function of 𝑓(𝑥) = 4𝑥. Then verify that both 𝑓(𝑓 −1 (𝑥)) and 𝑓 −1 (𝑓(𝑥)) are equal to
the identity function.
1
CP1: Find the inverse function of 𝑓(𝑥) = 5 𝑥. Then verify that both 𝑓(𝑓 −1 (𝑥)) and 𝑓 −1 (𝑓(𝑥)) are
equal to the identity function.
1
Name: ____________________________________
PreCalculus Notes Chapter 1 – Functions and Their Graphs
Date:___________________
***Important!***
EX2. FINDING INVERSE FUNCTIONS INFORMALLY
Find the inverse function of 𝑓(𝑥) = 𝑥 − 6. Then verify that both 𝑓(𝑓 −1 (𝑥)) and 𝑓 −1 (𝑓(𝑥)) are equal
to the identity function.
CP2: Find the inverse function of 𝑓(𝑥) = 𝑥 + 7. Then verify that both 𝑓(𝑓 −1 (𝑥)) and 𝑓 −1 (𝑓(𝑥)) are
equal to the identity function.
2
Name: ____________________________________
PreCalculus Notes Chapter 1 – Functions and Their Graphs
Date:___________________
3
Name: ____________________________________
PreCalculus Notes Chapter 1 – Functions and Their Graphs
Date:___________________
EX. 3 VERIFYING INVERSE FUNCTIONS ALGEBRAICALLY
Show that the functions are inverses of each other.
𝑓(𝑥) = 2𝑥 3 − 1
3
𝑔(𝑥) = √
𝑥+1
2
CP3: Show that the functions are inverses of each other.
𝑓(𝑥) = 𝑥 5
5
𝑔(𝑥) = √𝑥
4
Name: ____________________________________
PreCalculus Notes Chapter 1 – Functions and Their Graphs
Date:___________________
EX. 4 VERIFYING INVERSE FUNCTIONS ALGEBRAICALLY
Which of these functions is the inverse function of 𝑓(𝑥)
𝑔(𝑥) =
𝑥−2
5
or
=
5
5
ℎ(𝑥) = + 2
𝑥
CP 4: Which of these functions is the inverse function of 𝑓(𝑥)
𝑔(𝑥) = 7𝑥 + 4
?
𝑥−2
or
=
ℎ(𝑥) =
𝑥−4
7
?
7
𝑥−4
5
Name: ____________________________________
PreCalculus Notes Chapter 1 – Functions and Their Graphs
Date:___________________
EX. 5 VERIFYING INVERSE FUNCTIONS GRAPHICALLY
3
𝑥+1
Verify that the functions 𝑓(𝑥) = 2𝑥 3 − 1 and 𝑔(𝑥) = √
2
are inverse functions of each other
graphically.
5
CP 5: Verify that the functions 𝑓(𝑥) = 𝑥 5 and 𝑔(𝑥) = √𝑥 are inverse functions of each other
graphically.
6