The function f(x) is a substitution cipher that replaces each letter in the input string with a corresponding letter from a predetermined set of letters.

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

The code above approximates the behavior of the function by implementing a substitution map that maps each letter to its corresponding substitution. Non-alphabetical characters are copied directly.