If f (x) = sqrt 1/2x-10+3, which inequality can be used to find the domain of f (x) ?

The answer:

Generally, if the function form is f (x) = sqrt (a (x)), so the domain can be found as showing in the method given beneath:

Df = { x such that a (x) ≥ 0 }

this means that the function a (x) must be positive or equal zero

in our case we have, f (x) = sqrt (1 / 2x - 10 + 3)

so the domain of this function is, Df = { x such that 1 / 2x - 10 + 3 ≥ 0 }

the inequality depends on the true form of the given term,

so it should be 1 / 2x - 10 + 3 ≥ 0