I am wondering how I could go about solving this functional equation:

f(x)-g(x)=f(g(x))

Is there a way to determine what f(x) and g(x) are? I just created this and have an answer, but I don't have any idea how I would solve this.

Question

I am wondering how I could go about solving this functional equation:

f(x)-g(x)=f(g(x))

Is there a way to determine what f(x) and g(x) are? I just created this and have an answer, but I don't have any idea how I would solve this.

aum · Answer

If we know one function we can perhaps try to determine the other function so that it satisfies the given condition.

kainui · Answer

I don't know if there's some way we can manipulate the currently given equation to get this, but here is another relation that holds if it helps:$$\LARGE g(f(x^x))=f(x)$$