Calculus (3rd Edition)

The domain of the function $$f(x)=2\sin x+3\cos x$$ is $R$ and it is continuous on its domain.
Since $2\sin x$ and $3\cos x$ are defined on the whole real line $R$ and are continuous, then the sum of them is defined on $R$ and is continuous (because the sum of two continuous functions is another continuous function). That is, the domain of the function $$f(x)=2\sin x+3\cos x$$ is $R$ and it is continuous on its domain.