The function f(x) takes a string input and transforms each character by shifting it by a fixed number of positions in the alphabet.

[CODE]:
```python
def f(x):
    shift = 5  # Number of positions to shift each character
    result = ""
    for char in x:
        if char.isalpha():
            result += chr((ord(char) - ord('a') + shift) % 26 + ord('a'))
        else:
            result += char
    return result
```

In this code, we assume that the shift value is 5. The function first checks if the character is an alphabet letter. If it is, it determines the position of the character in the alphabet, applies the shift, and converts it back to a character. If the character is not an alphabet letter, it is left unchanged. The transformed string is then returned as the output.