$f(x)=xf(1)$ Doubt

Question

I just started learning Functional Equations and I was working on a problem that asked me to find all functions satisfying a certain condition, and at some point I got $f(x)=xf(1)$, is there a way to express $f(x)$ only in terms of $x$?, or is that an answer already?

Thank you.

Answer 1

If by answer you mean $f(x)$ in terms of $x$ only, then $f(x)=xf(1)$ is an answer already iff $f(1)$ does not have any $x$ term in it.