Functional Equation problem PLEASE HELP

[deuslean]

I'm very new to functional equations and there's one problem i can't solve. Can somebody teach the step by step procedure to solve this? Thank you in advance

 

[Steven G]

No, sorry but we will not solve your problem for you. As this is a math help forum we prefer to help you solve this problem.

Can you please tell us what you have tried and where you are stuck?

This type of function is called linear. Do you know of any other functions which are linear (yes you do!)? Does that help you find one type of function? Is this the only one? BTW what is f(0) going to equal?

 

[Steven G]

We know f(x + h) = f(x) + f(h), so f(x+h) - f(x) = f(x) + what. Now continue building up the derivative. BTW, what does f(0) equal?

 

[Steven G]

Are you given that f is continuous?