[SOLVED] Function Iteration

Hey, I'm new here. I've been thinking about a problem I've had in my mind, and I can't see to figure out where to begin to solve it. Anyway, here goes:

Define f(x) such that f(f(x)) = x^2 + k. Now, two things about this:

1. Is there anyway to find f(x)? Will f(x) be at least an algebraic or transcendental function?

2. Say f(x) isn't a 'nice' function. Is there any way to approximate f(x) at any point x by using some sort of approximation technique?

My background in math is not that great; I've basically got everything up to basic one-variable calculus covered, but no algebra, no real or complex analysis, etc. Am I going to have to learn this stuff in order to delve deeper into this? Thanks a lot for your help.