What is the Value of f(43) for a Function with a Period of 12?

[Aya]

I can someone pleas help me with this problem? Thanks.

A periodic function f has a period of 12. If f(7)=-2 and f(11)=9, determine the value of f (43)

how do you do this?

 

[eigenglue]

Well, 43 - 7 = 36.

 

[dav2008]

If f(x) has a period of a that means f(x)=f(x+na) where n is an integer.

Can you figure out the problem using that fact?

 

[Aya]

^ I don't get it can u show me an example?
or would it be like this

f(x)=f(x+na)
f (43)=f(7+12(-2))
f(43)=-17

 

[dav2008]

It just means that if the period is 12 then f(43)=f(43+n*12) where n is an integer.

So f(43)=f(43+12)=f(43-12)=f(43+24)...

In your example you say that f(43)=f(7+12(-2)). This is true but it means that f(43)=f(-17).

You are given f(7) and f(11). Can you relate one of those to f(43) somehow?

 

[Aya]

f(7)=-2

f(7)=(7+12+12+12)
=f(43)

so f(43)=-2

is that right, what about f(11)? or do i not need to use that?

 

[dav2008]

Yes that's right.

You found out f(43) so I don't know why you're worried about f(11).

 

[Aya]

^ ok, thanks