CSIR UGC NET June 2019 Part B Question 25

Question

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous and one-one function. Then which of the following is true?

1. $f$ is onto

2. $f$ is either strictly decreasing or strictly increasing

3. there exists $x \in \mathbb{R}$ such that $f(x)=1$

4. $f$ is unbounded