#### Answer

The domain of the function
$$ f(x)=2\sin x+3\cos x $$
is $ R $ and it is continuous on its domain.

#### Work Step by Step

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.