1. The problem statement, all variables and given/known data Give an example of a function f:R^2 -> R such that f(av) = a(f(v)) for all a in R and all v in R^2 but f is not linear. 2. Relevant equations f(v + w) = f(v) + f(w) (Additivity) 3. The attempt at a solution I really can't think of a function that will satisfy these properties. I know that for this to work, homogeneity must hold but additivity must not. I tried several functions, but none worked. Any hints? Thanks.