Question

f f (x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?
StartRoot one-half x EndRoot greater-than-or-equal-to 0
One-half x greater-than-or-equal-to 0
One-half x minus 10 greater-than-or-equal-to 0
StartRoot one-half x minus 10 EndRoot + 3 greater-than-or-equal-to 0

Answer 1

You must have the radicand nonnegative. So use
(1/2)x - 10 ≥ 0.
Solving gives (1/2)x ≥ 10 → x ≥ 20, so the domain is [20, ∞).