# Very important

Very important....

Let R denote the set of real numbers. Find all nondecreasing continuous
functions g : R R such that

g(x+g(y))=g(g(x))+g(y) for all x,y∈R

## Answers and Replies

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HallsofIvy
Homework Helper
And why is that "very important"?

tiny-tim
Homework Helper
Looks monotonous to me …

Looks monotonous to me …
I think u see it easy.....

I read this problem in abook,and I liked it
so can you solve it???

Looks monotonous to me …
And why is that "very important"?

I read this problem in abook,and I liked it
so can you solve it???

tiny-tim
Homework Helper
Hi vip89!

Hint: try differentiating with respect to x, and y, separately.

HallsofIvy
Homework Helper
Oh, I see. That hint didn't seem to make much sense until I did!

(Funny how often that happens.)

tiny-tim
Homework Helper
Oh, I see. That hint didn't seem to make much sense until I did!

(Funny how often that happens.)
Oh my goodness! Does it work?

I didn't actually try it!

......

oh.......I cant solve it.!!
can u send me the answer??I need it quickly and there is no time to solve it because I have final exams

Thankx very much

tiny-tim
Homework Helper
… I have final exams
Hi vip89!

It's because you have final exams that you need to practise the technique …in case it comes up!

(and if it doesn't come up … why are you bothered? )

So … differentiating with respect to x … what do you get?

I have acomption with my friend ,who find the answer first

Redbelly98
Staff Emeritus
Homework Helper
I am going to stay with the topic as given in the subject line here.

Why is the competition with your friend important?

ok , it is not important
can u solve it ,pls??

HallsofIvy
Homework Helper
Wouldn't that be cheating?

Redbelly98
Staff Emeritus
Homework Helper
ok , it is not important
can u solve it ,pls??
Actually no, I can't. But I do have some advice for you.

In this forum, you'll pretty much never get other people to solve entire problems for you. People like to see some attempt that you tried to solve it first. So far you haven't done that.

Did you try the suggestion from tiny-tim in message #6 ? If not, then try it. If you did try it then explain how far you got with it, or why you were unable to get very far with it, or just what you don't understand.

And lastly, welcome to physicsforums.com

ok
I will try
and I want to say that is not cheating because It is not homework

That is wt I did:

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