how to verify if $e^x$ is homogeneous or not? i think it's not homogeneous because there's no y...

Question

lgbasallote · Answer

@phi can you help me here instead? :D

phi · Answer

f(x)= e^x
f(tx)= e^(tx) = (e^x)^t
which is not the same as t e^x
so no, it is not homogeneous

lgbasallote · Answer

but it can be turned into $$e^t + e^x$$ right? does it make any difference?

phi · Answer

This can be confusing (I always think twice about these things).  But no.
If we replace e with 2 (for easy reckoning) we can see
2^(2*3)= 2^6= 64
2^2 + 2^3= 4+8 =12 

but (2^2)^3= 4^3 = 64

lgbasallote · Answer

oops oh yeah lol it was $e^{x+y} = e^xe^y$ lol