Composite Functions

Composite FunctionsO 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”

Composite FunctionsO 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) + 3O = 10x – 8 + 3O f(g(x)) = 10x - 5

Composite FunctionsO Try it again with a harder one.O f(x) = x2 + x + 3 and g(x) = x + 4O Find f ○ gO f(g(x)) = (x + 4)2 + (x + 4) + 3O = x2 + 8x + 16 + x + 4 + 3O f(g(x)) = x2 + 9x + 23

Plug “g” into “f”FoilCombine like terms

Composite FunctionsO 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) + 2O = 8x – 28 + 2O g(f(x)) = 8x - 26

Composite FunctionsO Try a harder one.O f(x) = 2x – 4 and g(x) = x2 - 2x + 5O Find g ○ f.O g(f(x)) = (2x – 4)2 – 2(2x – 4) + 5O = 4x2 – 8x - 8x + 16 – 4x + 8 +

5O g(f(x)) = 4x2 – 20x + 29

Plug “f” into “g”FoilCombine like terms

Composite FunctionsO Now try some with just numbers.O f(x) = x2 – 7 and g(x) = 5 – x2

O Find f(g(1)) and g(f(3)).O g(1) = 5 – 12

O = 5 – 1O = 4O f(4) = 42 – 7O = 16 – 7O f(g(1) = 9

O f(3) = 32 - 7O = 9 – 7O = 2O g(2) = 5 - 22

O = 5 – 4O g(f(3) = 1

Composite FunctionsO Remember to break each step down.O Don’t get overwhelmed by the sight

of the problems.