Question

Identify The domain of the rational function, g(x)= 1/x+3

A (-∞, ∞)
B (-∞, 3)U(3, ∞)
C (-∞, -3]U[-3, ∞)
D (-∞, -3)U(-3, ∞)

Answer 1

The domain is (-∞ , -3) ∪ (-3, ∞) ⇒ D

Explanation:

The domain of the rational fraction is the values of x which make the fraction defined. That means the domain does not contain the values of x which make the denominator equal to 0.

∵ g(x) =
`(1)/(x+3)`

∴ The denominator = x + 3

→ Equate the denominator by 0

∵ x + 3 = 0

→ Subtract 3 from both sides

∴ x + 3 - 3 = 0 - 3

∴ x = -3

→ That means the domain can not have -3 because it makes the denominator

equal to 0

∴ The domain is all values of real numbers except x = -3

∴ The domain = {x : x ∈ R, x ≠ -3}

∴ The domain = (-∞ , -3) ∪ (-3, ∞)