- #1

spaghetti3451

- 1,344

- 34

## Homework Statement

I've been trying to solve the following problem but can't wrap my head around it.

Let ##x##, ##f(x)##, ##a##, ##b## be positive integers. Furthermore, if ##a > b##, then ##f(a) > f(b)##. Now, if ##f(f(x)) = x^2 + 2##, then what is ##f(3)##?

## Homework Equations

## The Attempt at a Solution

Well, the table illustrates my current understanding of the problem:

x-------------------f(x)-------------------f(f(x))

1-------------------??-------------------3

2-------------------??-------------------6

3-------------------??-------------------11

4-------------------??-------------------18

5-------------------??-------------------27

6-------------------??-------------------38

7-------------------??-------------------51

8-------------------??-------------------66

9-------------------??-------------------83

10-------------------??-------------------102

##f(x)## is a monotonic function, and is allowed to take integer values, so this means that the values in the third column must be interspersed in the second column in the order in which they appear in the third column.

That's how far I can take my intuition.