Question

Please help me determine whether the given function is homogeneous.

f(x,y)=cos(x^2/(x+y))

Answer 1

\[f(x,y)=\cos(\frac{ x^2 }{ x+y })\]

Answer 2

\[f(tx,ty)=\cos(\frac{ t^2x^2 }{ tx+ty })\]

Answer 3

\[=\cos(t \frac{ x^2 }{ x+y })\]

Answer 4

is it 'not homogeneous' because you can't factor the (t) out of cosine?

Answer 5

f(tx,ty) does not equal (t^n)f(x,y) making it not homogeneous...
correct?