Exercise
Determine if the following function:
f(x,y)=5
Is homogeneous.
Final Answer
Solution
f(x,y)=5
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)=
=5=
=t^0\cdot 5=
=t^0f(x,y)
We got
f(tx,ty)=t^0f(x,y)
Hence, by definition, the given function is homogeneous of degree 0.
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