Question:
The domain of the function f(x) = log \((x^2-4)\) is:
The domain of the function f(x) = log \((x^2-4)\) is:
Updated On: Mar 27, 2026
- [2,∞)
- (-∞,-2) U (2,∞)
- (2,∞)
- (-∞, -2] U (-2, −1)
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The Correct Option is B
Solution and Explanation
To find the domain of the function \( f(x) = \log(x^2-4) \), we need to ensure the argument of the logarithm is positive.
The expression \( x^2-4 \) must be greater than zero:
\( x^2-4 > 0 \)
Solve the inequality:
\( x^2 > 4 \)
This implies:
\( x > 2 \) or \( x < -2 \)
The solution provides the domain as a union of two intervals:
\((-∞, -2) \cup (2, ∞)\)
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