3.3 Inverse Functions and Relations
Obj: To determine the inverse of a relation or function and to graph a function and its inverse
Inverse Relations: Two relations are inverse relations if and only if one relation
contains the element (𝑏, 𝑎) whenever the other relation contains the element (𝑎, 𝑏)
[translation: switch x & y]
Example
*Functions also have inverses, but the inverse may not always be a function
Recall: The inverse of 𝑓(𝑥) is written 𝑓(𝑥)−1 if it is a function!
Graph 𝑓(𝑥 ) = 𝑥 3 and its inverse:
Graph 𝑓(𝑥 ) = 𝑥 2 + 2
Then find the inverse and graph it
***Notice the inverse graph is the reflection of 𝑓(𝑥) over the line 𝑦 = 𝑥
You try….
1) Find the inverse of 𝑦 = 0.5𝑥 − 8
(Hint: change 0.5 to ½ )
2) Sketch the following function and it’s inverse. Then tell if the inverse is a function.
𝑦 = (𝑥 + 3)3
3) Sketch the following function and it’s inverse. Then tell if the inverse if a function?
𝑦 = (𝑥 + 2)2 − 5
4) Sketch the following function and it’s inverse. Then tell if the inverse if a function?
𝑦 = ±√𝑥 − 1 + 3
5) Sketch the following function and it’s inverse. Then tell if the inverse if a function?
𝑦 = ±2√𝑥 + 3 − 6
p.130/ 13-23 odds 25, 26, & 31
31) Academics: Beth’s physics class, the lab work score counts the same as a test score
when the grades are averaged for the quarter. No other scores are used to find the
average grade. She scored 75%, 80%, and 72% on her tests. What lab work score must
she receive to average 80% for the quarter.