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

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Homework Help Overview

The discussion revolves around a periodic function with a period of 12, where the values of the function at specific points are given. The original poster seeks to determine the value of the function at f(43) based on the known values of f(7) and f(11).

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the concept of periodicity and how it applies to the function. There are attempts to relate the known values of the function to the desired value at f(43) using the periodicity property.

Discussion Status

Some participants have provided insights into the periodic nature of the function and how to manipulate the known values to find f(43). The discussion has progressed with various interpretations of the periodicity concept, and some participants have expressed uncertainty about the relevance of additional known values.

Contextual Notes

The original poster has provided specific values for the function at f(7) and f(11), but there is no indication of how these values might relate to each other or to the periodicity beyond the immediate context of finding f(43).

Aya
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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?
 
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Well, 43 - 7 = 36.
 
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?
 
^ 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
 
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?
 
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?
 
Yes that's right.

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

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