Homogeneous Functions – Homogeneous check to the function x in the power of y – Exercise 7048


Determine if the following function:


Is homogeneous.

Final Answer

The function is not homogeneous


We look at the function:


By definition, a function is homogeneous of degree n if and only if the following holds:


For a parameter t.



We plug in our function and get


We open brackets and get



And we got the following:

\neq t^nf(x,y)

For any t and any n.

In short, we got the following:

f(tx,ty)\neq t^nf(x,y)

Hence, by definition, the given function is not homogeneous.

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