A simple question on continuous functions Let me ask a simple question on continuous functions.
Let f be a continuous function from R to R.
$ f:X\rightarrow Y$
$f(5)=0$ and $f(6) = 1$
Then can you expect that:
for all y in the open interval $(0,1)$, 
some $x∈(5,6)$ exists such that $f(x)=y$.
If some points are unclear, let me correct them.
Thank you in advance.

Yes this is just an extension of the Intermediate value theorem which states:If $f:[a,b] \to \mathbb{R}$ is a continuous function and $y$ is such that $f(a) \leq y \leq f(b)$, then there exists $x \in [a,b]$ such that $f(x)=y$. 
Hence we can conclude:
$$\forall y \in (f(5),f(6)), \exists x \in (5,6)\ \text{such that} f(x)=y.$$
