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

Am I misinterpreting this question?  It seems too easy, this has a solution when x = 4.

f_0(4) = 8
f_1(4) = sqrt(4^2 + 6*8) = sqrt(64) = 8
etc.

I feel like I must be missing the point...

Posted by tomarken on 2006-11-19 11:17:32