Adorkable Group Title 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

1. hartnn Group Title

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

2. Adorkable Group Title

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 Group Title

yes.

4. hartnn Group Title

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

5. Adorkable Group Title

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

6. hartnn Group Title

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 Group Title

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

8. hartnn Group Title

n can be any natural number .

9. hartnn Group Title

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

10. Adorkable Group Title

not quite sure im understanding.

11. hartnn Group Title

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

12. hartnn Group Title

no?

13. hartnn Group Title

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 Group Title

Okay I got everything except the f(7)

15. Adorkable Group Title

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

16. hartnn Group Title

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

17. hartnn Group Title

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

18. Adorkable Group Title

sotheanswer coulve been -5 or -2?

19. hartnn Group Title

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

20. Adorkable Group Title

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

21. hartnn Group Title

for the same periodic function ?

22. Adorkable Group Title

yes

23. hartnn Group Title

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

24. Adorkable Group Title

11

25. Adorkable Group Title

So it can be plus or minus?

26. hartnn Group Title

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

27. hartnn Group Title

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

28. Adorkable Group Title

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 Group Title

f(95)

30. hartnn Group Title

yes, try it ..

31. Adorkable Group Title

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

32. hartnn Group Title

yes, ver correct :)

33. Adorkable Group Title

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

34. Adorkable Group Title

Thats impossible. Lol. Sorry but thankyou!

35. hartnn Group Title

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