Question

Atividades sobre funções compostas

Answer 1

Explicação passo-a-passo:

1)

• f(g(x)) = f(x - 2)

f(g(x)) = 3.(x - 2) + 1

f(g(x)) = 3x - 6 + 1

f(g(x)) = 3x - 5

• g(f(x)) = g(3x + 1)

g(f(x)) = 3x + 1 - 2

g(f(x)) = 3x - 1

a)

f(g(5)) = 3.5 - 5

f(g(5)) = 15 - 5

f(g(5)) = 10

b)

g(f(-2)) = 3.(-2) - 1

g(f(-2)) = -6 - 1

g(f(-2)) = -7

c)

f(g(x)) = f(x - 2)

f(g(x)) = 3.(x - 2) + 1

f(g(x)) = 3x - 6 + 1

f(g(x)) = 3x - 5

d)

g(f(x)) = g(3x + 1)

g(f(x)) = 3x + 1 - 2

g(f(x)) = 3x - 1

2)

a)

• f(g(x)) = f(x + 1)

f(g(x)) = (x + 1)² - 2.(x + 1)

f(g(x)) = x² + 2x + 1 - 2x - 2

f(g(x)) = x² - 1

• f(g(1)) = 1² - 1

f(g(1)) = 1 - 1

f(g(1)) = 0

b)

• g(f(x)) = g(x² - 2x)

g(x)) = x² - 2x + 1

• g(f(2)) = 2² - 2.2 + 1

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

g(f(2)) = 1

c)

f(g(f(x))) = f(x² - 2x + 1)

f(g(f(x))) = (x² - 2x + 1)² - 2.(x² - 2x + 1)

f(g(f(4))) = (4² - 2.4 + 1)² - 2.(4² - 2.4 + 1)

f(g(f(4))) = (16 - 8 + 1)² - 2.(16 - 8 + 1)

f(g(f(4))) = 9² - 2.9

f(g(f(4))) = 81 - 18

f(g(f(4))) = 63

d)

• f(f(x)) = f(x² - 2x)

f(f(x)) = (x² - 2x)² - 2.(x² - 2x)

• f(f(-1)) = [(-1)² - 2.(-1)]² - 2.[(-1)² - 2.(-1)]

f(f(-1)) = (1 + 2)² - 2.(1 + 2)

f(f(-1)) = 3² - 2.3

f(f(-1)) = 9 - 6

f(f(-1)) = 3