Finding $f(x)$ given a function $f : \Bbb N \to \Bbb N$ which satisfies $f\circ f(x) + f(x) = 2x+15$ I'm stuck on rewriting the function $f\circ f(x) + f(x) = 2x+15$ (into $f(x) = \dots)$. The answer given is $f(x) = x + 5$, which I can easily verify, but I do not know how to go about forming this aside from just trial and error. How would I go about doing this systematically?

It is also given that $f : \Bbb N \to \Bbb N$ is injective.
A reasonable thing to guess is that $f(x)$ is a polynomial. However, if the leading term is $x^n$, you get a leading term on the LHS of $x^{n^2}$ vs the leading term on the RHS of $x$. This means $n=1$ if a polynomial is going to work. So then we try $f(x)=ax+b$ and solve for the unknown coefficients.
does this naive argument work? 

let $f(x) = y.$ $f(f(x)) + f(x) = 5$  implies  $f(y) + y = 5$ for all $y$ in the range of $f.$