C4 Functions

Part iii.

It is obvious by inspection which is what I did and just stated functions u and v (they are also just stated in the mark scheme). However, is there a way to manipulate the functions in order to find u and v, perhaps in terms of f and/or g? I have only been able to get this but nothing from there:

$ug(x) = fu(x)$

Just trying to answer this a little bit more formally.