Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function such that $f(x) \neq x$ for any $x \in \mathbb{R}$ and $f(0)=1$. Then

• Correct answer
  A

  there exists $x \in \mathbb{R}$ such that $f(x) \gt 2$
• Correct answer
  B

  $f$ may have more than one zeros
• C

  $f$ has a unique zero
• D

  $f(x) \leq 2$ for all $x \in \mathbb{R}$

Hence, the correct answer is options: 'A', 'B'.