The function f(x) appears to be a substitution cipher on alphabetic characters, where each character is replaced by another character in a predefined manner. Case is ignored and the characters mapping remains same irrespective of the case, while numbers and other special characters remain unchanged.

[CODE]: 
```python
def substitute_cipher(input_str):
    substitution_map = {
        'a': 'f', 'b': 'v', 'c': 'd', 'd': 'h', 'e': 'x', 'f': 'l', 'g': 'e',
        'h': 't', 'i': 'k', 'j': 'g', 'k': 'j', 'l': 'p', 'm': 'q', 'n': 'y',
        'o': 'a', 'p': 'b', 'q': 'r', 'r': 's', 's': 'c', 't': 'w', 'u': 'm',
        'v': 'n', 'w': 'z', 'x': 'o', 'y': 'i', 'z': 'u'
    }
    output_str = ''
    for char in input_str:
        if char.isalpha():
            output_str += substitution_map[char.lower()]
        else:
            output_str += char
    return output_str
```