Define a sequence of functions f₀, f₁, f₂, ......, by

f₀(x)= 8, for all real x, and
f_n+1(x) = sqrt(x² + 6f_n(x)); for all real x and all non-negative integers n.

Solve the equation

f_n(x)= 2x

(In reply to re: Solution? by Richard)

Well, for f_n(x) = 2x to hold for all n, it must hold for n=0.  Since f_0(x) = 8 for all x, then the only solution for x is 4. 

That's why this question seemed way too easy...you don't even have to use the more complicated part of the sequence to solve for x, other than to verify that it does indeed work for all other values of n...

Posted by tomarken on 2006-11-19 12:14:56