Which of the following is not a homogeneous function?

Step-by-step solution

A function f(x, y) is homogeneous of degree n if f(tx, ty) = t^n f(x, y) for all t > 0 and some real n . Function A: f(tx, ty) = (ty)^2 + 2(tx)(ty) = t^2(y^2 + 2xy) = t^2 f(x, y) , homogeneous of degree 2. Function B: f(tx, ty) = 2(tx) - 3(ty) = t(2x - 3y) = t f(x, y) , homogeneous of degree 1. Function C: f(tx, ty) = ( ty tx ) = ( y x ) = f(x, y) , homogeneous of degree 0. Function D: f(tx, ty) = (tx) + (ty) cannot be expressed as t^n( x + y) for any n . For example, with t = 2 , f(2x, 2y) = (2x) + (2y) 2^n( x + y