To determine the domain of the function [tex]\( g(x) = \sqrt{x} + 7 \)[/tex], we need to identify the set of all [tex]\( x \)[/tex]-values for which the function is defined. Let's break this down step by step:
1. Examine the function components:
- The function [tex]\( g(x) \)[/tex] consists of two parts: the square root function [tex]\( \sqrt{x} \)[/tex] and a constant term [tex]\( 7 \)[/tex].
2. Identify the constraints on [tex]\( \sqrt{x} \)[/tex]:
- The square root function [tex]\( \sqrt{x} \)[/tex] is defined only for non-negative values of [tex]\( x \)[/tex]. Mathematically, this means [tex]\( x \)[/tex] must be greater than or equal to 0:
[tex]\[
x \geq 0
\][/tex]
3. Combine the constraints:
- Since [tex]\( 7 \)[/tex] is a constant and does not impose any additional constraints on the domain, the domain of [tex]\( g(x) \)[/tex] is determined solely by the requirement that [tex]\( x \)[/tex] be non-negative.
4. Express the domain in interval notation:
- The set of all [tex]\( x \)[/tex]-values that satisfy [tex]\( x \geq 0 \)[/tex] can be written in interval notation as:
[tex]\[
[0, \infty)
\][/tex]
Thus, the domain of the function [tex]\( g(x) = \sqrt{x} + 7 \)[/tex] is:
[tex]\[
\boxed{[0, \infty)}
\][/tex]
