To determine the domain of the function [tex]\( g(x) = \frac{x+6}{2} \)[/tex], we need to identify all values of [tex]\( x \)[/tex] for which the function is defined.
Let's analyze the given function step-by-step:
1. Function Analysis:
- The function [tex]\( g(x) = \frac{x+6}{2} \)[/tex] involves basic arithmetic operations: addition and division.
2. Checking for Restrictions:
- Addition: The term [tex]\( x + 6 \)[/tex] is a simple linear expression involving [tex]\( x \)[/tex] and the constant 6. There are no restrictions related to this addition since it is defined for all real numbers.
- Division: The denominator of the fraction is 2, which is a constant, non-zero number. Division by a non-zero constant does not impose any restrictions on the values of [tex]\( x \)[/tex].
3. Conclusion:
- Since [tex]\( x + 6 \)[/tex] is defined for all real numbers and the division by 2 does not introduce any restrictions (as the denominator is never zero), the function [tex]\( g(x) = \frac{x+6}{2} \)[/tex] is defined for all real numbers.
Therefore, the domain of [tex]\( g(x) \)[/tex] is all real numbers.
[tex]\[
\text{Domain of } g(x) = \frac{x+6}{2} \text{ is } \mathbb{R} \text{ or equivalently, } (-\infty, \infty).
\][/tex]
