Answer
$f(x)$ is continuous over the interval $(0, \infty).$
Work Step by Step
There are no restrictions on the numerator but there restrictions are on the denominator and, therefore, it decides the interval over which the function is continuous.
Since the radicand cannot be negative and the denominator cannot be zero $\to x\gt0\to$ the function $f(x)$ is continuous over the interval $(0, \infty).$
