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Nady [450]
2 years ago
11

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

Mathematics
1 answer:
8_murik_8 [283]2 years ago
4 0

Answer:

The domain is (-∞ , -3) ∪ (-3, ∞) ⇒ D

Step-by-step explanation:

<em>The domain of the rational fraction is t</em><em>he values of x which make the fraction defined</em><em>. That means </em><em>the domain does not contain the values of x which make the denominator equal to 0</em><em>.</em>

∵ g(x) = \frac{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, ∞)

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