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Question
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.
Options
R – {3, – 2}
R – {–3, 2}
R – [3, – 2]
R – (3, – 2)
Solution
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is R – {3, – 2}.
Explanation:
Given that: f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)`
f(x) is defined if x2 – x – 6 ≠ 0
⇒ x2 – 3x + 2x – 6 ≠ 0
⇒ (x – 3)(x + 2) ≠ 0
⇒ x ≠ – 2, x ≠ 3
So, the domain of f(x) = R – {– 2, 3}
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