Probably I'm just being stupid but: According to Wikipedia. * Additivity (also called the superposition property): f(x + y) = f(x) + f(y). This says that f is a group homomorphism with respect to addition. * Homogeneity of degree 1: f(αx) = αf(x) for all α. f[x_] := x + 2; f[3 + 7] f + f 5*f f[5*10] 12 14 60 52 which indicates x+2 is not linear but obv it is a linear function. Where is the error?