Determine whether the function has y-symmetry or origin symmetry : `f(x) = x/(e^(x)-1)+x/2 + 1`

Explanation

To determine whether the function \( f(x) = \frac{x}{e^{x} - 1} + \frac{x}{2} + 1 \) has y-symmetry or origin symmetry, we will follow these steps:

### Step 1: Check for y-symmetry
To check for y-symmetry, we need to see if \( f(-x) = f(x) \).

1. **Calculate \( f(-x) \)**:
\[
f(-x) = \frac{-x}{e^{-x} - 1} + \frac{-x}{2} + 1
...