The domain of definition of the function $y = 3e^{x-1}\log(x-1)$ is
Step-by-Step Solution
Key Concept: The domain of a composite function is the intersection of individual domain restrictions
The function $f: (1, \infty)$ has domain restriction. We find $x^2 - 1 \geq 0$, which gives $x^2 \geq 1$, so $x \in (-\infty, -1] \cup [1, \infty)$. For the intersection with the given domain $(1, \infty)$, we get $x \in (1, \infty)$. Additionally, $x - 1 > 0$ gives $x > 1$, so $x \in (1, \infty)$ from constraint (2). Combining constraints (1) and (2), the domain is $x \in (1, \infty)$.
Correct Answer: 1