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Sec. 2.6

Sec. 2.6. Combinations of Functions. Arithmetic Combinations of Functions. Sum, Difference, Product, and Quotient of Functions Sum (f + g)(x) = f(x) + g(x) Difference (f – g )(x) = f(x) – g(x) Product (fg)(x) = f(x) • g(x) Quotient (f/g)(x) = f(x)/g(x)

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Sec. 2.6

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  1. Sec. 2.6 Combinations of Functions

  2. Arithmetic Combinations of Functions • Sum, Difference, Product, and Quotient of Functions • Sum (f + g)(x) = f(x) + g(x) • Difference (f – g )(x) = f(x) – g(x) • Product (fg)(x) = f(x) • g(x) • Quotient (f/g)(x) = f(x)/g(x) • Domains: consist of all real numbers common to both domains.

  3. Ex. 1 p. 229 • f(x) = 2x + 1 g(x) = x2 +2x – 1 Find (f+g)(x) Ex. 2 p. 230 Find (f – g)(x) then evaluate when x = 2

  4. Any restrictions on the domain of f and g must be considered. Ex. 6 Quotient f(x) = √x g(x) = √(4-x2) • (f/g)(x) b) ( g/f)(x)

  5. Ex. f(x) = 3x2 + 2 g(x) = 2x a) Find (f + g)(-1) b) (f/g)(2)

  6. Composition of Functions f(g(x)) denoted (f ◦ g)(x) • Means some value x is put in the function g, then the solution to that is placed in the function f. • The domain of f ◦ g is the set in the domain of g such that g(x) is in the domain of f.

  7. Ex. 7 f(x) = x + 2 g(x) = 4 – x2 a)Find (f ◦ g)(x) b) (g ◦ f)(x)

  8. Ex Find (f ◦ g)(x) for f(x) = 3x2 + 2 and g(x) = 2x

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