What is the domain of ?

To find the domain of this function, find the parts of the function that cannot exist/would make the function unsolvable. For example, since we are working within the reals, we cannot have a negative number under the square root sign. That means that x-2≥0 →x≥2.

At the same time, a 0 in the denominator of a fraction makes the entire fraction undefined so must make it so that the denominator cannot be 0 (x-5≠0). Therefore x≠5. Combining these criteria, we have all real numbers such that x≥2 and x≠5.