1. Operations with functions

2. Example 7-2a

3. A quick review: Functions have a domain (input) and a range (output). f(x) = {(1, 4), (2, 6), (5, 3)} Domain: {1, 2, 5} Range : {4, 6, 3} f(2) = 6 f(1) = 4 Domain Range 1 2 5 4 6 3

4. With composite functions, the output of one function becomes the input of another function. f(x) x g(f(x)) f g 9 3 10 17 4 16 26 25 5 g(x) = x + 1 f(x) = x2 g(f(x)) = x2 + 1 g o f = x2 + 1

5. f(x) = {(9, 4), (7, 7), (0, –1)} g(x) = {(7, 0), (–1, 7), (4,9)} = f(g(x)) } Example 7-3a

6. Iff(x) = {(1, 2), (0, –3), (6, 5), (2, 1)} and g(x) = {(2, 0), (–3, 6), (1, 0), (6, 7)}, find g(5) is undefined g(f(x)) Example 7-3c

7. = 12x2 – 12x + 3 – 2x + 1 + 4 Example 7-4a

8. Example 7-4a