It inserts the character '8' after the first character of the input string and repeats the second character as the third character.

[CODE]: 
```python
def approx_f(x):
    return x[0] + '8' + x[1] * 2 + x[2:]
```

To validate this description and the provided code, let's test the function on more inputs.

COMMAND: PYTHON(./temp/function.py "uvwxyz" "example" "function" "coding" "Python")