The function is continuous on its entire domain.
The domain of
is the open interval
For each point, a, in that interval, f is the quotient of two continuous functions -- with a nonzero denominator -- and is therefore continuous.
Find the "breaks" in the domain
Functions will often have inputs that, for lack of a better word, "break" the function. For functions of the form
For your function,
Since the variable is in the denominator, we can set the denominator equal to zero and find that restriction, in this case
But, since the variable is also under a square root,
When you look at the domain for your function,