1. Lesson 5-5: Inverse Functions and Relations
Advanced Math Topics

2. Property of Inverse Functions
Two functions f and g for which:
f(a) = b and g(b) = a
* these can also be written as f(a) = b and f -1(b) = a

3. To write the equation of the inverse for each function:
Replace f(x) with y. Switch x and y.
Solve for y. Replace y with f -1(x).

4. Example #1- would be f(x) = x - 5
y = x – 5
x = y – 5
x = y
x + 5 = y
f -1(x) = x +
x x

5. Graphing functions and their inverses
when (a,b) is on the graph of a function, then __________ is on the graph of the inverse
The ___________ is the reflection of the graph over the line ________.
(b, a)
inverse
y = x

6. An inverse _____________________
An inverse _____________________. On a graph you can use a _______________ to determine whether a _____________ is also a function.
Horizontal Line Test: If a ____________ crosses the graph more than once, then the function’s inverse _______________.
may or may not be a function
Horizontal line test
inverse
horizontal line
does not exist
*** do the horizontal line test on the original function

7. 1. Make an x/y chart for f(x) graph the points and connect the dots
To Graph a function and it’s inverse (put this on the blank space at the bottom of the page)
1. Make an x/y chart for f(x) graph the points and connect the dots
2. Make an x/y chart for f-1(x) by switching the x and y coordinates and then graph and connect the dots

8. Example 1: Find and Graph an inverse function
Find the inverse of
Graph f(x) and f-1(x)

9. Examples Cont…
graph the function and its inverse

10. Inverse Functions
Two functions f and g are inverse functions if and only if both of their compositions are the identity function.
[f o g](x) = x and [g o f](x) = x
So, if you plug g into f and simplify you get x and if you plug f into g and simplify you get x
BOTH have to give x for functions to be inverses

11. Determine if the functions are inverses

12. Determine if the functions are inverses