Question

Determine o dominio da função

a) f(X) = x + 1/x³ - 4x

b) f(x) = 4x/6x² + 13x - 5

Answer 1

O denominador deve ser diferente de zero

a)

x³ - 4x ≠ 0

x(x² - 4) ≠ 0

x ≠ 0

ou

x² - 4 ≠ 0

x² ≠ 4

x ≠ ±2

D = ℝ - {-2, 0, 2}

b)

6x² + 13x - 5 ≠ 0

Δ = 13² - 4 * 6 * (-5)

Δ = 169 + 120 = 289

$x = \frac{ - 13± \sqrt{289} }{2 \times 6}$

$x = \frac{ - 13± 17 }{12}$

$x' = \frac{ - 13 + 17 }{12}$

$x' = \frac{ 4 }{12}$

$x' = \frac{ 1 }{3}$

$x'' = \frac{ -13 - 17 }{12}$

$x'' = \frac{ - 30 }{12}$

$x'' = - \frac{ 5 }{2}$

D = ℝ - {-5/2, 1/3}