The function takes an input string, inserts the first character in the middle of the string, and then repeats that character. More specifically, it splits the input string in half, puts the first character between the two halves, and then adds the first character again at the end of the string.

[CODE]: Here's a Python code that approximates the behavior of the function:

```python
def f(x):
    middle_idx = len(x) // 2
    return x[:middle_idx] + x[0] + x[middle_idx:] + x[0]
```