One one and continuous function from $\Bbb R$ to $\Bbb R$ Let $f :\mathbb R \to \mathbb R$ be a continuous and one one function. Then which of the following is true?


*

*f is onto.

*f is either strictly increasing or strictly decreasing.

*There exist $x \in \Bbb R$ such that $f (x) = 1$

*f is unbounded

1, 3 and 4 are not true.
The function $f(x) = \tan^{-1}x + 10$ is a counterexample for all of them.  
2 is true.
To show this, assume the contrary and derive a contradiction using intermediate value theorem.
