The function f(x) processes an input string in the following manner: 
1. Iterate over each character from the second character to the second-last character. 
2. For each character, if the character is an alphabet and appears more than once, replace it with the next character in the alphabet.
3. Add the following character to the end of the input string: if the first character in the input string is 'a', append 'j'; otherwise, append the next character from the first character.

[CODE]:
```python
def f(x):
    if len(x) < 2:
        return x[:-1] + chr(ord(x[-1]) + 1)

    new_x = x[0]
    for char in x[1:-1]:
        if x.count(char) > 1 and char.isalpha():
            new_x += chr(ord(char) + 1)
        else:
            new_x += char

    if x[0] == 'a':
        new_x += 'j'
    else:
        new_x += chr(ord(x[0]) + 1)

    return new_x
```

Please verify whether the given code behaves similarly to the provided function.