Answer:
![\large \boxed{ \boxed{ \tt x \geqslant 2 \: \: is \: \: the \: \: domain \: \: of \: \: function}}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7B%20%5Cboxed%7B%20%5Ctt%20x%20%5Cgeqslant%202%20%5C%3A%20%20%5C%3A%20is%20%5C%3A%20%20%5C%3A%20the%20%5C%3A%20%20%5C%3A%20domain%20%5C%3A%20%20%5C%3A%20of%20%5C%3A%20%20%5C%3A%20function%7D%7D)
Step-by-step explanation:
We are given the square root function below:
![\large{g(x) = \sqrt{x - 2} }](https://tex.z-dn.net/?f=%20%5Clarge%7Bg%28x%29%20%3D%20%20%5Csqrt%7Bx%20-%20%202%7D%20%7D)
Recall that domain is the set of all x-values and that a number inside the square root cannot be negative.
From the given square root function above, substituting x >= 2 gives a positive output. But if we substitute x < 2, evaluating the numbers inside result in negative number in the square root which does not exist in Real Number.
Hence,
![\large{y = \sqrt{x - a} }](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20%20%5Csqrt%7Bx%20-%20a%7D%20%7D)
And thus, the domain is
![\large \boxed{x \geqslant a}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7Bx%20%5Cgeqslant%20a%7D)
Since if x < a, the output would become an imaginary number.
From the given function,
![\large{g(x) = \sqrt{x - 2} }](https://tex.z-dn.net/?f=%20%5Clarge%7Bg%28x%29%20%3D%20%20%5Csqrt%7Bx%20-%202%7D%20%7D)
From the form of sqrt(x-a) where domain is a-term which is 2.
Since a = 2, and thus
![\large \boxed{x \geqslant 2}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7Bx%20%5Cgeqslant%202%7D)