Homogeneous Functions – Homogeneous check to a constant function – Exercise 7041

Exercise

Determine if the following function:

f(x,y)=5

Is homogeneous.

Final Answer

 The function is homogeneous of degree 0

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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