1. 3.7-1 Inverse Functions

2. Just as with algebra, we may undo certain parts of a function Most often, we apply the inverse of some new function

3. Relations If R is a relation, then the inverse of R (R -1 ), is the set: – R -1 = {(b,a) | (a, b) ε R} In simpler terms, to find the inverse, we flip the x-and-y values – Be mindful of when you have sets, and when you have a graph to work with

4. Example. Determine the inverse of the following relation. Then, graph the relation and determine the domain and range. {(4, -1), (-3,2), (0,5), (9,8)} Flip x and y New relation?

5. Example. Find the inverse of the relation {(1, 5), (2, 7), (3, 8), (4, 10)}. Graph the inverse, and determine the domain and range.

6. Equations If you have an equation, such as y = x 2, then we will still exchange the x and y coordinates/values. Create a small table or use test points as before

7. Example. Find the inverse of the equation y = x 2, and graph. Determine the domain and range of the inverse.

8. Horizontal Line Test For any given function, f(x), we can determine if an inverse functions exists using a test Horizontal Line Test = if a horizontal line only touches the graph of the function f(x) in one spot, then an inverse function will exist What test is this similar too?

9. If an inverse function does not exist, we can look to restrict the domain to create an inverse – Use only values which would allow us to pass the horizontal test

10. Example. Determine if the function f(x) = (x-2) 2 has an inverse. Graph?

11. Example. Determine if the function f(x) = 3x – 5 has an inverse.

12. Assignment Pg. 282 1-21 odd