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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”

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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 g(f(x)) = 4 – (x + 2) 2 = 4 – (x 2 + 4x + 4) = -x 2 – 4x

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

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

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Operations on Functions Lesson 3.5. Sums and Differences of Functions If f(x) = 3x + 7 and g(x) = x 2 – 5 then, h(x) = f(x) + g(x) = 3x + 7 + (x 2 – 5)

Operations on Functions Lesson 3.5. Sums and Differences of Functions If f(x) = 3x + 7 and g(x) = x 2 – 5 then, h(x) = f(x) + g(x) = 3x + 7 + (x 2 – 5)

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