QuestionFind $(f \circ g)(x)$ and its domain in interval notation for $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$.

Studdy Solution
Write the domain in interval notation.
The domain of $(f \circ g)(x)$ in interval notation is $(-\infty, -7) \cup (-7, -6) \cup (-6,6) \cup (6,7) \cup (7, \infty)$.
So, the composite function $(f \circ g)(x)=\frac{13}{49-x^{2}}$ and its domain is $(-\infty, -7) \cup (-7, -6) \cup (-6,6) \cup (6,7) \cup (7, \infty)$.