To perform a reflection of the function \( f(x) = |x| + 2 \) across the x-axis, we take the negative of the entire function.
Thus, the transformation for \( g(x) \) is:
\[ g(x) = -(|x| + 2) \]
To break that down, we can rewrite it as:
\[ g(x) = -|x| - 2 \]
So, the equation of \( g(x) \) will be:
\[ g(x) = -|x| - 2 \]
If you need it in the same format as you provided (using placeholders), it could look like:
\[ g(x) = -|x| - 2 \]
where \( \text{insert required symbols} \) would be done in the context of defining the reflection across the x-axis.
If you want to write it in the structure of your initial question:
\[ g(x) = -|x| - 2 \]
This indicates that you are reflecting \( f(x) \) across the x-axis and then translating it down by 2 units.