2
$\begingroup$

it is obvious that if $f$ is an affine function, then $f$ has this property: there exist two function $g$ and $h$ such that $f(t+s)=g(t)+h(s)$ for all $t,s \in\mathbb{R}$. My question is: is there any non-affine function which has this property. In other words, is this property a characterisation of affine functions or not?

1 Answers 1