Função composta

A = B = C = N =

B A C A N A

1

2

3

4

A

f(x) = x + 1 f: A B

2

3

4

5

B

g(y) = y2

g: B C

4

9

16

25

C

g ( y ) = y 2

f(x) f(x)

g(f(x)) = (f(x))2 g (f(x)) = (x + 1)2

(g o f)(x) = (x+1)2

(g o f)(1) = (1+1)2

(g o f)(3) = (3+1)2

(g o f)(2) = (2+1)2

(g o f)(4) = (4+1)2 f(1) = 2

f(2) = 3

1) f(x) = 3x – 2 g(x) = 4x + 1 g(f(x)) = ? ou (g o f) (x) = ?

g(x) = 4x + 1

f(x) f(x)

g(f(x)) = 4 (3x – 2) + 1

(g o f) (x) = 12x – 8 + 1

(g o f) (x) = 12x – 7

2) f(x) = x2 – 1 g(x) = x + 2

(f o g) (x) = ?

f(x) = x2 – 1

g(x) g(x)

(f o g) (x) = (x + 2)2 – 1(f o g) (x) = (x2 + 4x + 2) – 1(f o g) (x) = x2 + 4x + 1

(g o f) (x) = x2 + 1

3) f(x) = x2 + 1 f(f(2)) = ?

f(2) = (2)2 + 1 f(2) = 4 + 1 f(2) = 5

f(5) = 52 + 1 f(f(2)) = 26

4) f(x) = 2x – 1 f(g(x)) = 6x + 11 g(x) = ?

f(x) = 2x – 1

g(x) g(x)

6x + 11 = 2 g(x) – 1

g(x) = 3x + 6

f(g(x)) = 2 g(x) – 1

6x + 11 + 1 = 2 g(x)6x + 12 = 2 g(x)

Página 58exercícios 48 até 51