Question

Dadas as funções f(x) = x2 – 4 g(x) = (x + 2) e h(x) = – x – 1,calcular:

1) f(2) – g(– 2) + h(– 1)
2) f(0) – g(0) – h(0)
3) f(x) + g(x) – h(x)
4) f(x) : g(x)
5) f(x) ∙ g(x) ∙ h(x)
6) [f(x)]2

Answer 1

Sejam as funções f(x), g(x) e h(x) dadas, temos que:

1) f(2) - g(-2) + h(-1)

f(2) = 2² - 4 = 0

g(-2) = (-2 + 2) = 0

h(-1) = -x - 1 = -(-1) - 1 = 0

f(2) - g(-2) + h(-1) = 0 - 0 + 0 = 0

2) f(0) - g(0) - h(0)

f(0) = 0² - 4 = -4

g(0) = (0 + 2) = 2

h(0) = -0 - 1 = -1

f(0) - g(0) + h(0) = -4 + 2 - 1 = -3

3) f(x) + g(x) - h(x)

x² - 4 + (x + 2) - (-x - 1)

= x² - 4 + x + 2 + x + 1

= x² + 2x - 1

4) f(x) : g(x)

(x² - 4) : (x + 2)

= (x + 2)(x - 2) : (x + 2)

= x - 2

5) f(x) · g(x) · h(x)

(x² - 4) · (x + 2) · (-x - 1)

= (x³ + 2x² - 4x - 8) · (-x - 1)

= -x⁴ - x³ - 2x³ - 2x² + 4x² + 4x + 8x + 8

= x⁴ - 3x³ + 2x² + 12x + 8

6) [f(x)]²

(x² - 4)²

= (x²)² - 2·x²·4 + 4²

= x⁴ - 8x² + 16