Question

The domain of the function $f(x) = \dfrac{\log_2 (x - 5)}{x^2 + 3x - 4}$ is:

• A. $(1,\infty)$
• B. $(10,\infty)$
• C. $(5,\infty)$
• D. $\mathbb{R} \setminus \{-4\}$
• E. $\mathbb{R} \setminus \{-4,1\}$

Hint:

Always check log condition first, then denominator restriction.

Answer 1

The Correct Option is C

Concept:
• $\log(x)$ is defined only when argument $> 0$
• Denominator $\neq 0$

Step 1: Log condition
\[ x - 5 > 0 \Rightarrow x > 5 \]

Step 2: Denominator condition
\[ x^2 + 3x - 4 = (x+4)(x-1) \neq 0 \] So $x \neq -4, 1$

Step 3: Combine conditions
\[ x > 5 \Rightarrow \text{automatically excludes } -4, 1 \]
Final Conclusion:
\[ (5,\infty) \]