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Adorkable

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.

  • one year ago
  • one year ago

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

    • one year ago
  2. Adorkable
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    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) ?

    • one year ago
  3. hartnn
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    yes.

    • one year ago
  4. hartnn
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    f(31) = f(31-12) = f(31-12-12) and so on...

    • one year ago
  5. Adorkable
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    Woah. Why would you subtract 12 twice or more times? And what do we figure out when we do that?

    • one year ago
  6. hartnn
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    because for every interval of 12, the function has same value.... so if i add or subtract 12, the value of function is same \(f(x\pm 12 )= f(x)\)

    • one year ago
  7. hartnn
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    more specifically \(f(x\pm n*12 )= f(x)\)

    • one year ago
  8. hartnn
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    n can be any natural number .

    • one year ago
  9. hartnn
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    so, f(43) = f(43-12) = f(31) = f(31-12) =.... do this till u get something you know the value of.

    • one year ago
  10. Adorkable
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    not quite sure im understanding.

    • one year ago
  11. hartnn
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    f(43) = f(31) u got this ?

    • one year ago
  12. hartnn
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    no?

    • one year ago
  13. hartnn
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    well, i'll write out steps, see if u get it \(f(43)=f(43-12)=f(31)=f(31-12)=f(19)=f(19-12)=f(7)=-2\)

    • one year ago
  14. Adorkable
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    Okay I got everything except the f(7)

    • one year ago
  15. Adorkable
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    Because 19-12 equals 7 but, then 7-12 is equal to -5

    • one year ago
  16. hartnn
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    but u already have f(7) = -2 so u get f(43) = -2

    • one year ago
  17. hartnn
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    and yes, f(-5) also equals -2

    • one year ago
  18. Adorkable
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    sotheanswer coulve been -5 or -2?

    • one year ago
  19. hartnn
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    no, not -5 . f(43) = f(7) = -2

    • one year ago
  20. Adorkable
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    hmm. Can we try another example please? say f(-1)?

    • one year ago
  21. hartnn
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    for the same periodic function ?

    • one year ago
  22. Adorkable
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    yes

    • one year ago
  23. hartnn
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    ok, f(-1) = f(-1+12) = ?

    • one year ago
  24. Adorkable
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    11

    • one year ago
  25. Adorkable
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    So it can be plus or minus?

    • one year ago
  26. hartnn
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    its f(11) yes, + or -12 ...

    • one year ago
  27. hartnn
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    f(-1) = f(11) = 9

    • one year ago
  28. Adorkable
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    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.

    • one year ago
  29. Adorkable
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    f(95)

    • one year ago
  30. hartnn
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    yes, try it ..

    • one year ago
  31. Adorkable
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    Would it be f(95)=f(11)=9 so far am i correct?

    • one year ago
  32. hartnn
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    yes, ver correct :)

    • one year ago
  33. Adorkable
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    Okay! Thank you once again so much for your patience and time!! Im going to best response all your answers!

    • one year ago
  34. Adorkable
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    Thats impossible. Lol. Sorry but thankyou!

    • one year ago
  35. hartnn
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    lol. welcome ^_^ and yes, thats not required and not possible...

    • one year ago
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