To solve this problem, let's carefully analyze the given function [tex]\( g \)[/tex] and understand its definition and implications.
The function [tex]\( g \)[/tex] is specified as follows:
[tex]\[ g(x) = -x \text{ if } x \neq 2 \][/tex]
### Step-by-Step Solution:
1. Understanding the Function Definition:
- The function [tex]\( g(x) \)[/tex] is defined as [tex]\( -x \)[/tex] for all [tex]\( x \)[/tex] except when [tex]\( x = 2 \)[/tex].
2. Implications of the Function Definition:
- Since [tex]\( g(x) \)[/tex] is defined as [tex]\( -x \)[/tex] when [tex]\( x \neq 2 \)[/tex], we understand that the value of the function can be determined straightforwardly by substituting [tex]\( x \)[/tex] into the expression [tex]\( -x \)[/tex].
3. Evaluating Examples:
- If [tex]\( x = 1 \)[/tex], then [tex]\( g(1) = -1 \)[/tex].
- If [tex]\( x = 0 \)[/tex], then [tex]\( g(0) = 0 \)[/tex].
- If [tex]\( x = -3 \)[/tex], then [tex]\( g(-3) = 3 \)[/tex].
- Note that the above calculations are valid as these values of [tex]\( x \)[/tex] are not equal to 2.
4. Special Case at [tex]\( x = 2 \)[/tex]:
- The function definition explicitly specifies the behavior for all [tex]\( x \neq 2 \)[/tex].
- There is no provided information on the behavior of [tex]\( g(2) \)[/tex]. So, to respect the defined domain of the function, we must acknowledge this gap but focus on the [tex]\( x \neq 2 \)[/tex] case as specified.
5. General Representation for [tex]\( x \neq 2 \)[/tex]:
- For any real number [tex]\( x \neq 2 \)[/tex], the value of the function [tex]\( g \)[/tex] is [tex]\( -x \)[/tex].
### Conclusion:
Therefore, for any real number [tex]\( x \neq 2 \)[/tex]:
[tex]\[ g(x) = -x \][/tex]
This concludes the solution by fully capturing the behavior and definition of the function [tex]\( g \)[/tex] as given in the problem.
