The function rotates the input string by one position in a circular fashion, swaps the first and second characters, and replaces the last character with the first character of the original input string.

[CODE]: 
```python
def f_approx(x):
    rotated_str = x[-1] + x[:-1]
    swapped_str = rotated_str[1] + rotated_str[0] + rotated_str[2:]
    final_str = swapped_str[:-1] + x[0]
    return final_str
```

Let's test this approximation on a couple more inputs to validate its behavior.

COMMAND: PYTHON(./temp/function.py "example" "test123")