1. September 27, 2012 Inverse of Functions Warm-up: f(x) = x 2 – 1 and Find the following compositions, then state the domain 1. (f o g)(x)2. (g o f)(x) CW 1.9: Pg. 99 #15-23odd, Pg. 90 #35, 37 Test Monday/Tuesday!

2. What are inverses? f -1 (x) Inverse of multiplication is__________________ Inverse of addition is______________________ Inverse of a square root is__________________ Inverse of squared is______________________ Inverse of the relation {(-5, 4), (-1, 5), (0, 2), (3, 4)} is:

3. Lesson 1.9 Graphs of Inverses – What do you notice? Make a table for each and graph their points. What do you notice about their points? f(x) = 2x – 3 f(x) = x 2, x ≥ 0

4. Finding the Inverse Function, f -1 (x), algebraically Find the inverse function of: f(x) = 3x + 2 1) Rewrite f(x) to y 2) Switch the x and y variables. 3) Solve for y

5. Show that the two functions are inverses algebraically and graphically

6. The composition of a function and its inverse will always equal x. Let f and g be two functions: Two functions are inverses if and only if: (f o g)(x) = x and (g o f)(x) = x

7. Verifying that the two functions are inverses: by using the composition, f(f -1 (x)) = x f(x) = 3x + 2 = x – 2 + 2 f(f -1 (x)) = x Show that the composition of f and f -1 equals x. Replace x in f(x) with (x – 2)/3 Simplify YAY!

8. Now go the other way… f(x) = 3x + 2 f -1 (f(x))

9. Ways to verify two functions are inverses The compositions of the two functions equal x: (f o g)(x) = x and (g o f)(x) = x The graph of the inverse function is a reflection of the graph of f over the y = x line. If the coordinates of the function are (a, b), the inverse function coordinates are (b, a).

10. Are the following functions two inverses of each other? Show/explain how to check. f(x) = 1 + 7x and

11. The inverses of function A and D are functions, but B and C are not. Why? Figure out a rule or a test that tells you whether or not it is a function. ABCDABCD

12. Fill out the chart to help organize our Unit 1 Test Use f(x) = x 2 – 9 to find the following ZerosDomainUse a graph to find the range and determine where it is increasing, decreasing, and/or constant.. InverseComposition of function and inverse Evaluating f(2x – 3)