Let $f: \mathbb{R} \mapsto \mathbb{R}$ be defined by $f(x)=[x]+\sqrt{x-[x]}$. Here, $[x]$ is the greatest integer function for $x \in \mathbb{R}$ and $\sqrt{y}$ is the positive square root of $y$ for $y \in \mathbb{R}^{+}$. Then

• A

  $f$ is differentiable everywhere
• Correct answer
  B

  $f$ is continous everywhere
• Correct answer
  C

  $f$ is bijective
• D

  $f$ is discontinous only at integer points

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