Discussion
The domain of the function \(f(x) = \frac{\log_{2}(x - 5)}{x^{2} + 3x - 4}\) , is
Answer: C
The domain is \((5, \infty)\).
Two conditions apply. The logarithm needs \(x - 5 \gt 0\), so \(x \gt 5\). The denominator must not be zero: \(x^{2} + 3x - 4 = (x + 4)(x - 1)\), so \(x \neq -4, 1\).
Both excluded values already lie outside \(x \gt 5\), so the domain is simply \((5, \infty)\).
\(\mathbb{R} \setminus \{-4, 1\}\) ignores the logarithm, \((1, \infty)\) includes values where \(x - 5 \leq 0\), and \((10, \infty)\) leaves out valid points such as \(x = 6\).
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