Question

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

Answer 1

@phi can you help me here instead? :D

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

oops oh yeah lol it was \(e^{x+y} = e^xe^y\) lol