Question

Consider the function \(f(x) := exp(x+a)exp(-x)\)
c) As a corollary, prove the functional equation \(exp(a+b) = exp(a) exp(b)\)

Answer 1

@satellite73 i have after this question one more question which is in your level, nobody was able to solve it until now from open study.. i hope you can help me

Answer 2

man that took me a long time sorry

Answer 3

:) i am sorry, our profs are merciless with their questions

Answer 4

start with
\[\exp(x+a)\exp(-x)=\exp(a)\] put \(a=m+n, -x=n\) and you get
\[\exp(-n+m+n)\exp(n)=\exp(m+n)\] or
\[\exp(m)\exp(n)=\exp(m+n)\]
it was as simple change of variables, one martini too long

Answer 5

if you want to do it nicer, replace \(a\) by \(a+b\) and \(-x\) by \(b\)

Answer 6

i knew it was a change and used up like 3 pieces of paper to get the right one.

Answer 7

i am very thankful to you Satellite even you needed so much time and effort for this question it was really terrible question :)

Answer 8

no problem, if my head was straight it would have been easier
hope it is clear

Answer 9

yes it looks clear, thank you very much..

Answer 10

@satellite73 take a look at this question if you would like, if its not so much time consuming for you, nobody replied it to this yet.
http://openstudy.com/users/tunahan#/updates/4fed040fe4b0bbec5cfc87c8