1. 6-1: Operations on Functions (Composition of Functions)
I can find the composition of functions

2. Composition of functions
Putting one function into another function

3. Composition of functions
Putting one function into another function Two ways of writing: f₀g(x) = f(g(x))

4. Composition of functions
Putting one function into another function Two ways of writing: f₀g(x) = f(g(x)) Replace the “x” in f(x) with “g(x)”

7. Ex: f(x) = 2x – g(x) = 4x

8. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) =

9. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x))

10. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x)

11. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2( ) – 5

12. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5

13. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5

14. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5 g₀f(x)

15. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5 g₀f(x) = g(f(x)) =

16. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5 g₀f(x) = g(f(x)) = 4( )

17. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5 g₀f(x) = g(f(x)) = 4(2x – 5)

18. Ex: f(x) = 2x – 5 g(x) = 4x f₀g(x) = f(g(x)) = f(4x) = 2(4x) – 5 = 8x – 5 g₀f(x) = g(f(x)) = 4(2x – 5) = 8x – 20

19. HW: all, all