1. Do Now: Given f(x) = 2x + 8 and g(x) = 3x 2 – 1 find the following. 1.) (f + g)(x) 2.) g(x – 2)

2. Academy Algebra II/Trig 6.1: Composite Functions HW: p.407-408 (16, 18, 22, 30, 34) Project Due Wednesday: 1/30 Quiz 2.1, 6.1, 6.2: Thursday 1/31

3. Compositions  Given two functions f and g, the composite function, denoted by and read f composed with g, is defined by

4. Suppose f(x) = 2x 2 – 3 and g(x) = 4x. Find the following. 1.)2.)

5. Suppose f(x) = 2x 2 – 3 and g(x) = 4x. Find the following. 3.)4.)

6. Suppose f(x) = 2x 2 – 3 and g(x) = 4x. Find the following. 5.)6.)

7. Suppose. Find and determine the domain.

8. Suppose and. Find and determine the domain.

9. Domain of  Domain of is the domain g(x) in the domain of f.

10. Academy Algebra II/Trig 6.2: One-to-one functions & Inverses Project Due Wednesday: 1/30 Test 2.1, 6.1, 6.2: Thursday 1/31

11. Verifying Inverses  If and, then f and g are inverses of each other.

12. Verify f and g are inverses of each other.

13. Graphs of inverses.  Inverses are a reflection over the line y = x. (Domain and range switch)

14. One-to-one  To have an inverse, a function needs to be one-to-one.  It must pass both the vertical line test and horizontal line test for the function to be one-to-one. Is one-to-one?

15. Find the inverse algebraically, if the inverse exists. 1.)

16. Find the inverse algebraically, if the inverse exists. 2.)

17. Find the inverse algebraically, if the inverse exists. 3.)