Answer:
The domain is (-∞ , -3) ∪ (-3, ∞) ⇒ D
Step-by-step 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) = [tex]\frac{1}{x+3}[/tex]
∴ 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, ∞)
