Today in Pre-Calculus

1
Today in Pre-Calculus

• Notes (no handout)
• Combining Functions Algebraically
• Composition of Functions
• Go over quiz
• Homework

2
Combining Functions Algebraically

• Let f and g be two functions with intersecting
  domains. Then for all values of x in the
  intersection, the algebraic combinations of f and
  g are defined by the following rules
• Sum (fg)(x) f(x) g(x)
• Difference (f-g)(x) f(x) - g(x)
• Product (fg)(x)f(x)g(x)

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Example

• Let f(x) 3x3 7 and g(x) x2 1. Find the
• Sum
• Difference
• Product
• Quotient

4
Composition of Functions

• Functions that are combined but not by using
  arithmetic operations
• Combined by applying them in order (be careful!)
• Let f and g be two functions such that the domain
  of f intersects the range of g. The composition
  f of g,
• (f?g)(x)f(g(x)).

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Example

• Let f(x) x2 4x 5 and g(x) 2x 3
• (f?g)(x) (2x-3)2 4(2x-3) -5 4x2 4x 8
• (f?g)(2) 0
• (g?f)(x) 2(x2 4x 5) 3 2x2 8x 13
• (g?f)(2) 11
• (g?g)(x) 2(2x- 3) 3 4x - 9

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Example

• (s?t)(x) b)(s?t)(2)
• c) (t?s)(x) d) (s?s)(x)
• e) (t?t)(x)

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Homework

• Pg. 124 1-17 odd, ignore the domain part of the
  directions