I can't figure out how to solve: $\forall t \in [0,1]$, $f((1-t)x+ty)=(1-t)f(x)+tf(y)$. I have proved that $f(0)=0$.
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$ f(x)=ax+b $ is a solution. – hamam_Abdallah Jan 25 '22 at 20:59
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Your function is both convex and concave so must be linear – Golden_Ratio Jan 25 '22 at 21:04