The function f(x) takes an input string and for each character, if it's a lowercase letter and not 'z', it increments the character to the next letter in the alphabet. If the character is 'z', it replaces it with 'o'. For uppercase letters, it replaces them with their uppercase counterparts. Other characters are left unchanged.

[CODE]:

def custom_func(s):
    result = ""
    
    for char in s:
        if 'a' <= char <= 'y':
            result += chr(ord(char) + 1)
        elif char == 'z':
            result += 'o'
        elif 'A' <= char <= 'Z':
            result += char.upper()
        else:
            result += char
            
    return result