Why is the period of f(ax + b) equal to b/a?

[physixguru]

Homework Statement

If f{x + p } = f{x} for all x..then p is called the period of the function.

This part is clear to me.Now the book says...

The period of the function f{ax + b} is b/a.Can someone lead me through.

Homework Equations

N/A

 

[tiny-tim]

Hi physixguru!

hmm … I think they must mean:

The period of a function f for which f{ax + b} = f{x} for all x is b/a. ​

EDIT: ooh … that's not right … thinks … I think they mean the same f, and it's p not b:

The period of f{ax + b} is p/a. ​

Hint: put g(x) = f(ax + b). Then … ?

 

[physixguru]

I need the xplanation.

 

[tiny-tim]

Hi! see edit of previous post.

™

 

[HallsofIvy]

If f is a function with period p, that is, if f(x+ p)= f(x) for all x, then f completes one period as x goes from 0 to p. g(x)= f(ax+ b) will complete a period as ax+ b goes from 0 to p. That is, from ax+ b= 0 so x= -b/a, to ax+ b= p so x= (p- b)/a that is a "distance" of (p- b)/a- (-b/a)= p/a- b/a+ b/a. If f has period p, then f(ax+ b) has period p/a, not b/a.

 

[physixguru]

Thats right...i was cured when you told me that it was p/a.
thnx all.