Let $f: \mathbb{R} \longrightarrow \mathbb{R}$ be a function given by $f(x)=\max \{1-x, 1+x, 2\}$. Then

• Correct answer
  A

  $f$ is strictly increasing in the interval $(1, \infty)$
• Correct answer
  B

  $f$ is continuous everywhere
• C

  $f$ is differentiable everywhere
• D

  the minimum value of $f$ is attained only at a finite number of points

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