Question

If \( f(x) = \ln(6 - |x^2 + x - 6|) \), then domain of \( f(x) \) has how many integral values of \( x \)

• A. 5
• B. 4
• C. Infinite
• D. None of these

Hint:

Always convert \(|f(x)| < k\) into double inequality.

Answer 1

The Correct Option is D

Concept: \[ \log(6 - |x^2 + x - 6|) \text{ is defined when } 6 - |x^2 + x - 6| > 0 \] \[ |x^2 + x - 6| < 6 \] \[ -6 < x^2 + x - 6 < 6 \] \[ 0 < x^2 + x < 12 \] Solving gives integer values: \[ x = -3, -2, -1, 0, 1, 2 \Rightarrow 6 \text{ values} \] Since 6 is not in options → None of these.