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1.8 Combinations of Functions: Composite Functions

1.8 Combinations of Functions: Composite Functions. The composition of the functions f and g is. “f composed by g of x equals f of g of x”. Ex. f(x) =. g(x) = x - 1. Find. of 2. Ex. f(x) = x + 2 and g(x) = 4 – x 2 Find:. f(g(x)) = (4 – x 2 ) + 2. = -x 2 + 6.

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1.8 Combinations of Functions: Composite Functions

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  1. 1.8 Combinations of Functions: Composite Functions The composition of the functions f and g is “f composed by g of x equals f of g of x”

  2. Ex. f(x) = g(x) = x - 1 Find of 2 Ex. f(x) = x + 2 and g(x) = 4 – x2 Find: f(g(x)) = (4 – x2) + 2 = -x2 + 6 g(f(x)) = 4 – (x + 2)2 = 4 – (x2 + 4x + 4) = -x2 – 4x

  3. Ex. Express h(x) = as a composition of two functions f and g. f(x) = g(x) = x - 2

  4. Find the sum, difference, and quotient of two functions. f(x) = 2x + 1 g(x) = x2 + 2x - 1 (f + g)(x) = 2x + 1 + x2 + 2x - 1 = x2 + 4x 2x + 1 - (x2 + 2x - 1) = -x2 + 2 (f - g)(x) =

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