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Função composta

Função composta. . . . . . . A =  B =  C =  N = . A. N. A. A. C. B. f(x). f(x). 4. 1 2 3 4. 2. g ( y ) = y 2. 9. 3. g(f(x)) = (f(x)) 2 g (f(x)) = (x + 1) 2. 4. 16. 5. 25. (g o f)(x) = (x+1) 2. (g o f)(1) = (1+1) 2. B. A. C.

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Função composta

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  1. Função composta

  2.      A =  B =  C =  N =  A N A A C B

  3. f(x) f(x) 4 1 2 3 4 2 g ( y ) = y 2 9 3 g(f(x)) = (f(x))2 g (f(x)) = (x + 1)2 4 16 5 25 (g o f)(x) = (x+1)2 (g o f)(1) = (1+1)2 B A C (g o f)(2) = (2+1)2 f(x) = x + 1 f: A  B g(y) = y2 g: B  C (g o f)(3) = (3+1)2 f(1) = 2 (g o f)(4) = (4+1)2 f(2) = 3

  4. 2) f(x) = x2 – 1 g(x) = x + 2 (f o g) (x) = ? • f(x) = 3x – 2 • g(x) = 4x + 1 • g(f(x)) = ? • ou • (g o f) (x) = ? g(x) g(x) f(x) f(x) f(x) = x2 – 1 g(x) = 4x + 1 (f o g) (x) = (x + 2)2 – 1 (f o g) (x) = (x2 + 4x + 2) – 1 (f o g) (x) = x2 + 4x + 1 g(f(x)) = 4 (3x – 2) + 1 (g o f) (x) = 12x – 8 + 1 (g o f) (x) = 12x – 7 (g o f) (x) = x2 + 1

  5. 3) f(x) = x2 + 1 f(f(2)) = ? 4) f(x) = 2x – 1 f(g(x)) = 6x + 11 g(x) = ? g(x) g(x) f(2) = (2)2 + 1 f(2) = 4 + 1 f(2) = 5 f(x) = 2x – 1 f(g(x)) = 2 g(x) – 1 f(5) = 52 + 1 f(f(2)) = 26 6x + 11 = 2 g(x) – 1 6x + 11 + 1 = 2 g(x) 6x + 12 = 2 g(x) g(x) = 3x + 6

  6. Página 58exercícios 48 até 51

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