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Composition of Functions

Composition of Functions. Chapter 1 Section 2 - Christina McInnis. Real World Application.

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Composition of Functions

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  1. Composition of Functions Chapter 1 Section 2 -Christina McInnis

  2. Real World Application ~The amount of time it takes to get to work depends on how much traffic there is, and the amount of traffic there is depends on what time of day it is.~If we call the amount of traffic C and the time of day t, then C is a function of t.~If we call the time it takes to get to work W, then W is a function of C.~Then we can view the amount of time it takes to get to work as depending on the time of day; that is, we can form the composite function W(C(t)).

  3. Given f(x) = 3x2 -4 , and g(x) = 4x + 5.find (f + g) (x) Step 1 :add f(x) and g(x) Step 2 :combine like terms (3x2 -4) + (4x+5) 3x2 + 4x + 1 Answer: 3x2 + 4x + 1

  4. Given f(x) = 3x2 -4 , and g(x) = 4x + 5. find (f - g) (x) Step 1 :subtract f(x) and g(x) Step 2 :combine like terms (3x2 -4) - (4x+5) 3x2 - 4x + 9 Answer: 3x2 - 4x + 9

  5. Given f(x) = 3x2 -4 , and g(x) = 4x + 5. find (f * g) (x) Step 1 :multiply f(x) and g(x) • Step 2 :distribute (3x2 -4)(4x+5) 3x2 (4x) = 12x3 3x2 (5) = 15x2 -4(4x) = -16x -4(5)= -20 Answer: 12x3 +15x2 -16x -20

  6. Step 1 :divide f(x) over g(x) Step 2 : Simplify 3x2 -4/ 4x + 5 Answer: 3x2 -4/ 4x + 5 Given f(x) = 3x2 -4 , and g(x) = 4x + 5.find (f /g) (x)

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