1. Thursday  Last Day for Test corrections  Retest 7:40am tomorrow

2. Thursday: Factor these 3 problems

3. Factor these 3 problems

6. Composition of Functions Section 1-8

7. Objectives  I can find the composition of one function with another function

8. Function Composition Notation This does not say “FOG” You read this “f composed with g of x”

9. Function Composition Notation Another way to write this is OR f[g(x)]

10. Function Composition Notation

11. Function Composition OR EX 1: f(x) = x 2 g(x) = x + 1 Start with g(x) and put that in to f(x) = (x + 1) 2 = x 2 + 2x + 1

12. Function Composition EX 2: f(x) = x + 2 g(x) = 4 – x 2 Start with g(x) and put that in to f(x) = (4 – x 2 ) + 2 = -x 2 + 6

13. Function Composition EX 3: f(x) = x 2 + 1 g(x) = 2x Start with g(x) and put that in to f(x) = (2x) 2 + 1 = 4x 2 + 1

14. evaluating with Function Composition (Numbers) EX 4: f(x) = x 2 + 1 g(x) = 2x Start with g(x) & find g(3). Put that answer in to f(x). g(3) = 6 f(6) = 37

15. MORE Function Composition EX 5: f(x) = x 2 - 4 g(x) = 4x - 1 a) f[g(-1)] b) g(f(2)) c) f[g(a + 1)] g(-1) = -5; f(-5) = 21 f(2) = 0; g(0) = -1 g(a+1)= 4(a+1)-1 = 4a+3; f(4a+3) = (4a+3) 2 – 4 = 16a 2 +24a+5

16. MORE Function Composition EX 5: f(x) = x 2 - 4 g(x) = 4x - 1 d) [f o g](x) g(x) = 4x – 1 so put this into f(x) for x (4x – 1) 2 - 4 16x 2 – 8x - 3

17. 6) For what values of “x” is f(g(x)) = 10 Given: f(x) = 2x and g(x) = x + 3 Start from the outside. Set f(x); 2x = 10 and solve. So x = 5. This means that g(x) = 5. x + 3 = 5; therefore x = 2 Check by seeing if: f(g(2)) = 10

18. Homework  WS 2-4