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Adorkable 2 years ago Periodic Functuions. A periodic Function f(x) has a period of 12. If f(7)=-2 and f(11)=9, determine the value of f(43). Please explain thoroughly.

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1. hartnn

since the function is periodic with period 12, f(43) = f(43-12) = f(31), did u get this ?

2. Adorkable

I think so. So if for example in the same context if the question was f(79) then it would be f(79 - 12) = f(67) ?

3. hartnn

yes.

4. hartnn

f(31) = f(31-12) = f(31-12-12) and so on...

5. Adorkable

Woah. Why would you subtract 12 twice or more times? And what do we figure out when we do that?

6. hartnn

because for every interval of 12, the function has same value.... so if i add or subtract 12, the value of function is same $$f(x\pm 12 )= f(x)$$

7. hartnn

more specifically $$f(x\pm n*12 )= f(x)$$

8. hartnn

n can be any natural number .

9. hartnn

so, f(43) = f(43-12) = f(31) = f(31-12) =.... do this till u get something you know the value of.

10. Adorkable

not quite sure im understanding.

11. hartnn

f(43) = f(31) u got this ?

12. hartnn

no?

13. hartnn

well, i'll write out steps, see if u get it $$f(43)=f(43-12)=f(31)=f(31-12)=f(19)=f(19-12)=f(7)=-2$$

14. Adorkable

Okay I got everything except the f(7)

15. Adorkable

Because 19-12 equals 7 but, then 7-12 is equal to -5

16. hartnn

but u already have f(7) = -2 so u get f(43) = -2

17. hartnn

and yes, f(-5) also equals -2

18. Adorkable

sotheanswer coulve been -5 or -2?

19. hartnn

no, not -5 . f(43) = f(7) = -2

20. Adorkable

hmm. Can we try another example please? say f(-1)?

21. hartnn

for the same periodic function ?

22. Adorkable

yes

23. hartnn

ok, f(-1) = f(-1+12) = ?

24. Adorkable

11

25. Adorkable

So it can be plus or minus?

26. hartnn

its f(11) yes, + or -12 ...

27. hartnn

f(-1) = f(11) = 9

28. Adorkable

Okay. I have an idea of what youre talking about. I'll try this one and can you see if it is correct for me? Same function.

29. Adorkable

f(95)

30. hartnn

yes, try it ..

31. Adorkable

Would it be f(95)=f(11)=9 so far am i correct?

32. hartnn

yes, ver correct :)

33. Adorkable

Okay! Thank you once again so much for your patience and time!! Im going to best response all your answers!

34. Adorkable

Thats impossible. Lol. Sorry but thankyou!

35. hartnn

lol. welcome ^_^ and yes, thats not required and not possible...

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