No Roots of Negatives

Over the real numbers, a square root accepts zero and positive numbers only. So for a rule like f(x) = √(x - 5), the inside must satisfy x - 5 >= 0. Solving gives x >= 5: the domain is 5 and every number above it.

This time the answer is an inequality, not a single excluded number. A whole stretch of inputs is refused, everything below 5.

Watch the sign when x has a negative coefficient. For g(x) = √(10 - 2x), solve 10 - 2x >= 0: subtracting 10 gives -2x >= -10, and dividing by -2 flips the sign, so x <= 5. Check with 0: the inside is 10, which is fine.