The function f(x) encrypts the input string using a Caesar Cipher with a fixed shift of 1, not affecting numbers or special characters. It treats uppercase and lowercase characters separately.

[CODE]: 

```python
def encrypt_caesar_cipher(text):
    encrypted_text = ''

    for char in text:
        if char.isalpha():
            shifted = ord(char) + 1
            if char.islower():
                if shifted > ord('z'):
                    shifted = ord('a')
            elif char.isupper():
                if shifted > ord('Z'):
                    shifted = ord('A')
            encrypted_text += chr(shifted)
        else:
            encrypted_text += char

    return encrypted_text
```