Question
Let $f(x)=\log \left(\frac{x-1}{x-2}\right)$ and$g(x)=\log (x-1)-\log (x-2) .$ Is $f=g ?$
Step 1
The function $f(x)$ is defined for $\frac{x-1}{x-2} > 0$. This implies that $x$ is less than 1 or $x$ is greater than 2. Therefore, the domain of $f(x)$ is $(-\infty, 1) \cup (2, \infty)$. Show more…
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