f(0) ≠ 0

f(1) = 3

f(x) * f(y) = f(x+y) + f(x-y)

1. Determine f(7).

Thanks for the help!

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- Apr 18th 2010, 08:48 PMloztsDiscrete Question
f(0) ≠ 0

f(1) = 3

f(x) * f(y) = f(x+y) + f(x-y)

1. Determine f(7).

Thanks for the help! - Apr 18th 2010, 10:15 PMemakarov
The same problem was discussed here.

- Apr 19th 2010, 05:28 AMloztsDidn't quite understand the responses
Yes, I saw this post and tried to do it out myself out of pure curiosity but had problems trying to do it, which is why I am asking. I am curious how it is done. Could you please elaborate on your answer?

- Apr 19th 2010, 06:23 AMPlato
- Apr 19th 2010, 07:33 AMlozts
I don't quite get how to determine f(7). I don't know if I am just over looking something or what. I tried to find f(7) going off of tonio's post, but didn't have much luck.

- Apr 19th 2010, 08:02 AMPlato
It is easy to see that:

$\displaystyle f(n+1)=3f(n)-f(n-1)$

$\displaystyle f(2)=3f(1)-f(0)=9$

$\displaystyle f(3)=3f(2)-f(1)=?$

$\displaystyle {\color{white}.}~~~~~~~ \vdots $

$\displaystyle f(7)=3f(6)-f(5)$. - Apr 19th 2010, 08:11 AMlozts
Thanks a lot, I completely overlooked that but wouldn't

$\displaystyle

f(2) = 3f(1) - f(0) = 9 - f(0) ??

$

since f(0) isn't equal to 0. - Apr 19th 2010, 08:19 AMPlato