The function takes a string input and replaces each alphabetical character with another corresponding character, while leaving non-alphabetical characters unchanged. 

[CODE]:
```python
def f(x):
    input_alphabet = "abcdefghijklmnopqrstuvwxyz"
    output_alphabet = "lrhdscuynfjikgvtoexzpaqwbm"
    trans_table = str.maketrans(input_alphabet, output_alphabet)
    return x.translate(trans_table)
```