[SOLVED] function

dwsmith

MHF Hall of Honor
Mar 2010
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Let f be a function such that \(\displaystyle f(n+1)=1-[f(n)]^2, \forall n\in\mathbb{Z}, n\geq0\). How would f(n+2) be expressed in terms of f(n)?
 
Nov 2009
517
130
Big Red, NY
Let f be a function such that \(\displaystyle f(n+1)=1-[f(n)]^2, \forall n\in\mathbb{Z}, n\geq0\). How would f(n+2) be expressed in terms of f(n)?
\(\displaystyle f(n+1)=1-[f(n)]^2\)

\(\displaystyle \implies f(n+2) = f\left\{(n+1)+1\right\}=1-[f(n+1)]^2 = 1 - \left\{ 1-[f(n)]^2 \right\}^2\)
 
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dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Ok that trumps the ... answer first posed.
 
Nov 2009
517
130
Big Red, NY
I don't disagree with that but when your response was first .... I was in disagreement.
Oh yeah that, haha.

When I am fairly certain I know the answer, I like to secure my position. (Evilgrin)

Cheers!