The function takes a string input and shifts each character in the string 7 positions forward in the alphabet. If the input is a digit, it remains the same.

[CODE]:

```python
def approx_f(x):
    shifted_string = ""
    for char in x:
        if char.isalpha():
            start = ord('a') if char.islower() else ord('A')
            shifted_string += chr((ord(char) - start + 7) % 26 + start)
        else:
            shifted_string += char
    return shifted_string
```