The function reverses the input string and doubles the character if the character is the same when reversed.

[CODE]:

```python
def f(x):
    result = ""
    for char in x[::-1]:
        if char == char[::-1]:
            result += char * 2
        else:
            result += char
    return result
```

To further validate, let's test some other inputs:

COMMAND: PYTHON(./temp/function.py "abcde" "AaBbCc" "12321" "-+-+")