Discrete Question

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April 18th 2010, 08:48 PM
lozts

Discrete 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!
April 18th 2010, 10:15 PM
emakarov

The same problem was discussed here.
April 19th 2010, 05:28 AM
lozts

Didn'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?
April 19th 2010, 06:23 AM
Plato

Quote:

Originally Posted by lozts

I looked over the responses on that post already but still couldn't really figure out the answer to either question. Could you please elaborate?

What about the other discussion did you not follow?
I consider those two replies a complete solution.
I wonder what more short of a complete ready to turn is reply do you need.
April 19th 2010, 07:33 AM
lozts

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.
April 19th 2010, 08:02 AM
Plato

It is easy to see that:
$f(n+1)=3f(n)-f(n-1)$
$f(2)=3f(1)-f(0)=9$
$f(3)=3f(2)-f(1)=?$
${\color{white}.}~~~~~~~ \vdots$
$f(7)=3f(6)-f(5)$ .
April 19th 2010, 08:11 AM
lozts

Thanks a lot, I completely overlooked that but wouldn't
$<br /> f(2) = 3f(1) - f(0) = 9 - f(0) ??<br />$

since f(0) isn't equal to 0.
April 19th 2010, 08:19 AM
Plato

Quote:

Originally Posted by lozts

$<br /> f(2) = 3f(1) - f(0) = 9 - f(0) ??<br />$

Yes that is correct?
$f(1)f(0)=f(1+0)+f(1-0)=6$ so $f(0)=?$

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