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(2): Solution? by tomarken)

The problem does not say that the same solution for x is required for each n.  Is there an x that is not 4 that satisfies the equation for some n? What is the solution set for each fixed n?

Posted by Richard on 2006-11-19 12:40:29