1. Composite Functions

2. O Finding a composite function simply means plugging one function into another function. O The key thing to remember is which way you are going. O f ○ g means plug “g” into function “f” O g ○ f means plug “f” into function “g”

3. Composite Functions O Given the functions f(x) = 2x + 3 and g(x) = 5x – 4, find the composite function f ○ g. O Plug g(x) into f(x) every where there is an “x”. O f(g(x)) = 2(5x – 4) + 3 O = 10x – 8 + 3 O f(g(x)) = 10x - 5

4. Composite Functions O Try it again with a harder one. O f(x) = x 2 + x + 3 and g(x) = x + 4 O Find f ○ g O f(g(x)) = (x + 4) 2 + (x + 4) + 3 O = x 2 + 8x + 16 + x + 4 + 3 O f(g(x)) = x 2 + 9x + 23 Plug “g” into “f” Foil Combine like terms

5. Composite Functions O Now try the other way. O f(x) = 2x – 7 and g(x) = 4x + 2 O Find g ○ f. O g(f(x)) = 4(2x – 7) + 2 O = 8x – 28 + 2 O g(f(x)) = 8x - 26

6. Composite Functions O Try a harder one. O f(x) = 2x – 4 and g(x) = x 2 - 2x + 5 O Find g ○ f. O g(f(x)) = (2x – 4) 2 – 2(2x – 4) + 5 O = 4x 2 – 8x - 8x + 16 – 4x + 8 + 5 O g(f(x)) = 4x 2 – 20x + 29 Plug “f” into “g” Foil Combine like terms

7. Composite Functions O Now try some with just numbers. O f(x) = x 2 – 7 and g(x) = 5 – x 2 O Find f(g(1)) and g(f(3)). O g(1) = 5 – 1 2 O = 5 – 1 O = 4 O f(4) = 4 2 – 7 O = 16 – 7 O f(g(1) = 9 O f(3) = 3 2 - 7 O = 9 – 7 O = 2 O g(2) = 5 - 2 2 O = 5 – 4 O g(f(3) = 1

8. Composite Functions O Remember to break each step down. O Don’t get overwhelmed by the sight of the problems.