Question

What is the domain of this function?

$f(x)= \sqrt{2x-14}$

Please explain and answer in interval notation

Answer 1

$2x-14\geq0\\\\ 2x\geq14\\\\ x\geq7\\\\ D_f:x\in\langle7,\infty)$

Answer 2

The square root function is only defined for non-negative arguments. So you must have

... 2x - 14 ≥ 0

... 2x ≥ 14

... x ≥ 7

In interval notation, x ∈ [7, ∞)