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1.4 building functions from functions

1.4 building functions from functions. Operations w/ 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 (x) = f(x) g g (x). Examples.

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1.4 building functions from functions

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  1. 1.4 building functions from functions

  2. Operations w/ 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 (x) = f(x) g g(x)

  3. Examples • For f(x) = 3x + 5, g(x) = 2x – 1, find the following with each domain. • 1. f(x) + g(x) • 2. f(x) – g(x) • 3. f(x)g(x) • 4. f(x) g(x)

  4. Examples • For f(x) = 9x, g(x) = 4x2 – 2, find the following with each domain. • 5. g(x) + f(x) • 6. g(x) – f(x) • 7. g(x)f(x) • 8. g(x) f(x)

  5. Composition of functions • Let f and g be 2 functions such that the domain of f intersects the range of g. • (f◦g)(x) = f(g(x)) • How to do: all x values in the 1st function get replaced by the entire 2nd function • Example: find (f◦g)(x) = f(g(x)) 1.f(x) = 2x – 1, g(x) = 4x + 3 f(g(x)) = 2(4x + 3) – 1 = 8x + 5 g(f(x)) = 4(2x – 1) + 3 = 8x - 1 2. f(x) = ex, g(x) = √x f(g(x)) = e√x g(f(x)) = √ex

  6. Examples • Find f(g(x)) and g(f(x)) and state each domain 9. f(x) = 3x + 2, g(x) = x – 1 10. f(x) = x2 – 2, g(x) = x + 1 11. f(x) = 1 , g(x) = 1 2x 3x

  7. Evaluating functions • Perform each operation and then evaluate each for the given value f(x) = 2x – 1, g(x) = x2 12. (f + g)(-2) 13. (f – g)(10) 14. (fg)(3) 15. g (-3) f 16. (f◦g)(5) 17. (g◦f)(-4)

  8. Homework • P. 116-117 #1-7 odd, 11-27 odd

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