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.



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hartnn
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since the function is periodic with period 12,
f(43) = f(4312) = f(31),
did u get this ?

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) ?

hartnn
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yes.

hartnn
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f(31) = f(3112) = f(311212) and so on...

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?

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
\(f(x\pm 12 )= f(x)\)

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

hartnn
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n can be any natural number .

hartnn
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so, f(43) = f(4312) = f(31) = f(3112) =....
do this till u get something you know the value of.

Adorkable
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not quite sure im understanding.

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

hartnn
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no?

hartnn
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well, i'll write out steps, see if u get it
\(f(43)=f(4312)=f(31)=f(3112)=f(19)=f(1912)=f(7)=2\)

Adorkable
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Okay I got everything except the f(7)

Adorkable
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Because 1912 equals 7 but, then 712 is equal to 5

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

hartnn
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and yes, f(5) also equals 2

Adorkable
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sotheanswer coulve been 5 or 2?

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

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

hartnn
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for the same periodic function ?

Adorkable
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yes

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

Adorkable
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11

Adorkable
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So it can be plus or minus?

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

hartnn
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f(1) = f(11) = 9

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.

Adorkable
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f(95)

hartnn
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yes, try it ..

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

hartnn
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yes, ver correct :)

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!

Adorkable
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Thats impossible. Lol. Sorry but thankyou!

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