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(6): Solution? by tomarken)

x=-4 does not work, in my opinion, because sqrt is normally taken to be nonnegative which means that f_n(x) cannot equal -8. Squaring both sides of f_n(x)=2x has caused an extraneous solution to appear, I believe.

Posted by Richard on 2006-11-19 20:40:39