Question

Determine whether or not the following function is homogeneous: $f(x,y)=\sqrt{x^2+2xy+3y^2}$
If homogeneous enter 1 else enter 0.

Answer 1

Consider, $f(x,y)=\sqrt{x^2+2xy+3y^2}$

$\Rightarrow f(tx,ty)=\sqrt{{\left(tx\right)}^2+2\left(tx\right)\left(ty\right)+3{\left(ty\right)}^2}$

$=\sqrt{t^2{x}^2+t^{2}2xy+t^{2}3y^2}$

$=t\sqrt{x^2+2xy+3y^2}$

$=tf(x,y)$

Hence this is homogeneous function of degree 1

Hence the answer is !.