Question

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.

Answer 1

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

Answer 2

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) ?

Answer 3

yes.

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

n can be any natural number .

Answer 9

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

Answer 10

not quite sure im understanding.

Answer 11

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

Answer 12

no?

Answer 13

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

Answer 14

Okay I got everything except the f(7)

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

sotheanswer coulve been -5 or -2?

Answer 19

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

Answer 20

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

Answer 21

for the same periodic function ?

Answer 22

yes

Answer 23

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

Answer 24

11

Answer 25

So it can be plus or minus?

Answer 26

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

Answer 27

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

Answer 28

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.

Answer 29

f(95)

Answer 30

yes, try it ..

Answer 31

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

Answer 32

yes, ver correct :)

Answer 33

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

Answer 34

Thats impossible. Lol. Sorry but thankyou!

Answer 35

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