1. Algebra 2: Section 7.4
Inverse Functions

2. Inverse Relation Maps the output back to original input
Domain of inverse is the range of the original function

3. Finding Inverse of a Function (Algebraically)
Rewrite function name; usually f(x) as y
Switch the x’s and y’s
Solve for y

4. Finding Inverse of a Function

5. Power Function A function of the form
Where a is a real number b is rational

6. Finding Inverse of a Function

7. Finding Inverse of a Function

8. Verifying Functions are Inverses
Functions are inverses of each other if…
f(g(x)) = x
AND
g(f(x)) = x
f -1(x) = g(x)
Reads “inverse of f”

9. Verify that f and g are inverses
f and g are inverses of each other!!!

10. Homework
P.426 #16-24 all
#25-31 odd

11. Inverse Functions (Day 2)
Algebra 2: Section 7.4
Inverse Functions
(Day 2)

12. Warm-Up What is the range of a function?
Output values
y-values
What is the domain of a function?
Input values
x-values

13. Finding Inverses of a Function (Graphically)
To create the inverse graph of a function…
Reflect the original graph across the line y = x.
Examples on Board!!!
Swap x and y values of plotted points
y = x y = x3
Sketchpad Example

14. Warm-Up
Write the image of each point after its reflection in the line y = x.
(2, 3) 
(-2, 4) 
(-1, -1) 
(1, -3) 

15. Inverse Functions
An inverse relation may or may not be a function (even if the original IS a function!)
Graph original in calculator (y1)
Graph inverse in calculator (y2)
Is the inverse a function?
How could you tell by looking at only the graph of the original function?

16. Horizontal Line Test Look at original function
If no horizontal line intersects the graph of the function more than once, then
the inverse of the original will also be a function
So, if a relation passes the vertical and horizontal line tests then the original relation and its inverse are functions
Vertical Line Test  original function
Horizontal Line Test  inverse function

17. Examples: Find the inverse

18. Homework P.427 #36-56 all Use graphing calculator for #48-56
Draw sketch of graph on homework

19. Verifying if Functions are Inverses
Using TI-83
Enter each function into Y1 and Y2
Enter Y1(Y2) into Y3
Enter Y2(Y1) into Y4
Turn on graph of Y3 only
See if it is the graph of y=x
Turn on graph of Y4 only
Verify #31, p.426 using TI-83