1. Do Now: Given f(x) = 2x + 8 and g(x) = 3x2 – 1 find the following.
1.) (f + g)(x)
2.) g(x – 2)

2. Academy Algebra II/Trig
6.1: Composite Functions
HW: p (16, 18, 23, 29, 30, 34)

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) = 2x2 – 3 and g(x) = 4x. Find the following.
1.) 2.)

5. Suppose f(x) = 2x2 – 3 and g(x) = 4x. Find the following.
3.) 4.)

6. Suppose f(x) = 2x2 – 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

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.)