Periodic function every differentiable with f(x+a) = Bf(x)

[ClipsClips99]

Hello all, I was wondering if someone can help on this problem:

A periodic function with period A satisfies f(x+a) = f(x) for all x in its domain. What can you conclude about a function which has a derivative everywhere and satisfies an equation of the form

f(x+a)= Bf(x)

for all x, where A and B are positive constants?

Any tips or hints are welcomed.

 

[stapel]

A periodic function with period A satisfies f(x+a) = f(x) for all x in its domain....

Surely the book said "period A" and "f(x + A)" (or "period a" and "f(x + a)"), so the variables matched...? :shock:

Eliz.