Homogeneous Functions – Homogeneous check to sum of functions with powers – Exercise 7062

Exercise

Determine if the following function:

$f(x,y)=x^2+y^2+3x$

Is homogeneous.

Final Answer

Show 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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