I was learning about angle systems and encountered this simple argument : $$90^o = 1 \text{ right angle }$$ $$\implies 1^o = \Bigg(\dfrac{1}{90}\Bigg)^{th} \text{ of a right angle}$$ Seems obvious, doesn't it? This got me wondering : "When do two quantities that are somehow related to each other follow the unitary method?"
Let's say that if first quantity is $x$, then the second quantity is given by a function, $f$. If they follow the unitary method, it means that for $n \in \Bbb R$, $f(nx) = n\cdot f(x)$. Now, for what kind of functions is this true?
I know that one of these might be : $f(x) = kx$ which would imply that $f(nx) = k(nx) = n(kx) = n\cdot f(x)$.
But, are other functions that satisfy this relation possible as well? If yes, please provide some examples and if no, is there some proof that no such function exists?
Thank You.