Exercise
Determine if the following function:
f(x,y)=x^2+y^2+3x
Is homogeneous.
Final Answer
Solution
f(x,y)=x^2+y^2+3x
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)=
=(tx)^2+(ty)^2+3(tx)=
=t^2\cdot x^2+t^2\cdot y^2+t\cdot 3x
We got
f(tx,ty)\neq t^rf(x,y)
Hence, by definition, the given function is not homogeneous.
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