Question

Determine whether or not following functions is homogeneous

$f(x,y)=x+ycos\frac{y}{x}$
If homogeneous enter 1 else enter 0

Answer 1

$f(x,y)=x+ycos\frac{y}{x}\Rightarrow f(tx,ty)=tx+tycos\frac{ty}{tx}=t(x+ycos\frac{y}{x})=tf(x,y)$
Hence this is a homogeneous function of degree 1