Question

find the domain of the function.
h(x)=\ln\left(\frac{1}{x - 1}\
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Explanation:

Step1: Analyze the condition for the logarithm

For the function \(y = \ln(u)\), the argument \(u>0\). Here \(u=\frac{1}{x - 1}\), so \(\frac{1}{x - 1}>0\).

Step2: Solve the inequality \(\frac{1}{x - 1}>0\)

Since the numerator \(1>0\), for the fraction \(\frac{1}{x - 1}>0\), we need the denominator \(x-1>0\).
Solving \(x - 1>0\) gives \(x>1\).

Answer:

The domain of the function \(h(x)\) is \((1,\infty)\)