Exercise
Determine if the following function:
f(x,y)=3x^my^n
Is homogeneous.
Final Answer
Solution
f(x,y)=3x^my^n
Function f is called homogeneous of degree r if it satisfies the equation:
f(tx,ty)=t^rf(x,y)
for all t.
f(tx,ty)=
=3{(tx)}^m{(ty)}^n=
=3t^mx^mt^ny^n=
=3t^{m+n}x^my^n=
=t^{m+n}f(x,y)
We got
f(tx,ty)=t^{m+n}f(x,y)
Hence, by definition, the given function is homogeneous of degree
m+n
Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions!