MathDB

Let

f:\mathbb{Q}\rightarrow \mathbb{Q}

a monotonic bijective function.
a)Prove that there exist a unique continuous function

F:\mathbb{R}\rightarrow \mathbb{R}

such that

F(x)=f(x),\ (\forall)x\in \mathbb{Q}

.
b)Give an example of a non-injective polynomial function

G:\mathbb{R}\rightarrow \mathbb{R}

such that

G(\mathbb{Q})\subset \mathbb{Q}

and it's restriction defined on

\mathbb{Q}

is injective.

Problem Statement