anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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hartnn
  • hartnn
since the function is periodic with period 12, f(43) = f(43-12) = f(31), did u get this ?
anonymous
  • anonymous
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) ?
hartnn
  • hartnn
yes.

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hartnn
  • hartnn
f(31) = f(31-12) = f(31-12-12) and so on...
anonymous
  • anonymous
Woah. Why would you subtract 12 twice or more times? And what do we figure out when we do that?
hartnn
  • 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 \(f(x\pm 12 )= f(x)\)
hartnn
  • hartnn
more specifically \(f(x\pm n*12 )= f(x)\)
hartnn
  • hartnn
n can be any natural number .
hartnn
  • hartnn
so, f(43) = f(43-12) = f(31) = f(31-12) =.... do this till u get something you know the value of.
anonymous
  • anonymous
not quite sure im understanding.
hartnn
  • hartnn
f(43) = f(31) u got this ?
hartnn
  • hartnn
no?
hartnn
  • hartnn
well, i'll write out steps, see if u get it \(f(43)=f(43-12)=f(31)=f(31-12)=f(19)=f(19-12)=f(7)=-2\)
anonymous
  • anonymous
Okay I got everything except the f(7)
anonymous
  • anonymous
Because 19-12 equals 7 but, then 7-12 is equal to -5
hartnn
  • hartnn
but u already have f(7) = -2 so u get f(43) = -2
hartnn
  • hartnn
and yes, f(-5) also equals -2
anonymous
  • anonymous
sotheanswer coulve been -5 or -2?
hartnn
  • hartnn
no, not -5 . f(43) = f(7) = -2
anonymous
  • anonymous
hmm. Can we try another example please? say f(-1)?
hartnn
  • hartnn
for the same periodic function ?
anonymous
  • anonymous
yes
hartnn
  • hartnn
ok, f(-1) = f(-1+12) = ?
anonymous
  • anonymous
11
anonymous
  • anonymous
So it can be plus or minus?
hartnn
  • hartnn
its f(11) yes, + or -12 ...
hartnn
  • hartnn
f(-1) = f(11) = 9
anonymous
  • anonymous
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.
anonymous
  • anonymous
f(95)
hartnn
  • hartnn
yes, try it ..
anonymous
  • anonymous
Would it be f(95)=f(11)=9 so far am i correct?
hartnn
  • hartnn
yes, ver correct :)
anonymous
  • anonymous
Okay! Thank you once again so much for your patience and time!! Im going to best response all your answers!
anonymous
  • anonymous
Thats impossible. Lol. Sorry but thankyou!
hartnn
  • hartnn
lol. welcome ^_^ and yes, thats not required and not possible...

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