MathDB

Let

\mathbb{R}

be the set of real numbers. Does there exist a function

f: \mathbb{R} \mapsto \mathbb{R}

which simultaneously satisfies the following three conditions?
(a) There is a positive number

M

such that

\forall x:

\minus{} M \leq f(x) \leq M. (b) The value of

f(1)

1

. (c) If

x \neq 0,

then f \left(x \plus{} \frac {1}{x^2} \right) \equal{} f(x) \plus{} \left[ f \left(\frac {1}{x} \right) \right]^2

Problem Statement