Domain of a Root

A radical function has its input under a root, like $f\left(x\right) = \sqrt{2x-10}$. Some inputs break it. With input 1 the inside is $2-10$, which is -8, and no real number squares to a negative. The domain is every input the rule accepts.

To find it, ask for the inside to be at least 0: $2x-10 \ge 0$. Move the -10 across to get $2x \ge 10$, then divide by 2: $x \ge 5$. The input 5 itself is allowed, since the square root of 0 is 0.

A cube root has no such limit. $cbrt\left(-8\right)$ is -2, because -2 cubed is -8. So $g\left(x\right) = cbrt\left(x-8\right)$ accepts every real input. Only an even root, like the square root, shuts out negatives.