Question

A function \[F(x,y)\] is homogeneous of degree \[n\] when which condition holds?

Options

• \[F(\lambda x,\lambda y)=\lambda^{n}F(x,y)\] for any non-zero constant \[\lambda\].

• \[F(\lambda x,\lambda y)=\lambda F(x,y)\] for every degree \[n\].

• \[F(x,y)=\lambda^{n}F(\lambda x,\lambda y)\] for any non-zero constant \[\lambda\].

• \[F(\lambda x,y)=\lambda^{n}F(x,y)\] for any \[\lambda=0\].

Answer 1

Homogeneity of degree \[n\] is defined by \[F(\lambda x,\lambda y)=\lambda^{n}F(x,y)\]. The condition is required for any non-zero constant \[\lambda\].