Question

If f(x)=x+7 and g(x)=1/x-13 what is the domain of (f times g)(x)

Answer 1

`(f\cdot g)(x)=f(x)\cdot g(x)\\\\\text{We have}\ f(x)=x+7\ \text{and}\ g(x)=(1)/(x-13).\\\\\text{Substitute}\\\\(f\cdot g)(x)=(x+7)\cdot(1)/(x-13)=(x+7)/(x-13)\\\\\text{The domain:}\\\\x-13\\eq0\qquad\text{add 13 to both sides}\\\\x\\eq13\\\\Answer:\ \boxed{x\in\mathbb{R}-\{13\}}\to\boxed{\text{All real numbers except 13}}`