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

The function $f$ is not onto; The arctangent function is an example.
2 is true
3 is false.  Shift the arctangent function up.
4 is false.  Again the arctangent function.
