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Adorkable

  • 3 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
    • 3 years ago
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    since the function is periodic with period 12, f(43) = f(43-12) = f(31), did u get this ?

  2. Adorkable
    • 3 years ago
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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) ?

  3. hartnn
    • 3 years ago
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    yes.

  4. hartnn
    • 3 years ago
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    f(31) = f(31-12) = f(31-12-12) and so on...

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

  6. hartnn
    • 3 years ago
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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 \(f(x\pm 12 )= f(x)\)

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

  8. hartnn
    • 3 years ago
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    n can be any natural number .

  9. hartnn
    • 3 years ago
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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.

  10. Adorkable
    • 3 years ago
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    not quite sure im understanding.

  11. hartnn
    • 3 years ago
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    f(43) = f(31) u got this ?

  12. hartnn
    • 3 years ago
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    no?

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

  14. Adorkable
    • 3 years ago
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    Okay I got everything except the f(7)

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

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

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

  18. Adorkable
    • 3 years ago
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    sotheanswer coulve been -5 or -2?

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

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

  21. hartnn
    • 3 years ago
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    for the same periodic function ?

  22. Adorkable
    • 3 years ago
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    yes

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

  24. Adorkable
    • 3 years ago
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    11

  25. Adorkable
    • 3 years ago
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    So it can be plus or minus?

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

  27. hartnn
    • 3 years ago
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    f(-1) = f(11) = 9

  28. Adorkable
    • 3 years ago
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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.

  29. Adorkable
    • 3 years ago
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    f(95)

  30. hartnn
    • 3 years ago
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    yes, try it ..

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

  32. hartnn
    • 3 years ago
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    yes, ver correct :)

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

  34. Adorkable
    • 3 years ago
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    Thats impossible. Lol. Sorry but thankyou!

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

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