Which of the following is not a homogenous function of x and y

Step-by-step solution

A function f(x, y) is homogeneous of degree n if f(tx, ty) = t^n f(x, y) for any non-zero constant t . For option (1), f(tx, ty) = ^2( ty tx ) + ty tx = ^2( y x ) + y x = t^0 f(x, y) , which is homogeneous of degree 0. For option (2), f(tx, ty) = 2(tx) - (ty) = t(2x - y) = t^1 f(x, y) , which is homogeneous of degree 1. For option (3), f(tx, ty) = (tx) - (ty) . Since (tx) - (ty) t^n( x - y) for any n , this function is not homogeneous. For option (4), f(tx, ty) = (tx)^2 + 2(tx)(ty) = t^2(x^2 + 2xy) = t^2 f(x, y) ,