Question

The domain of the function f(x) = log \((x^2-4)\) is:

• A. [2,∞)
• B. (-∞,-2) U (2,∞)
• C. (2,∞)
• D. (-∞, -2] U (-2, −1)

Answer 1

The Correct Option is B

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:

\((-∞, -2) \cup (2, ∞)\)