Let $f: R \rightarrow R$ be a function defined by $f(x)=\operatorname{Min}\{x+1,|x|+1\}$. Then which of the following is true?

• A

  $f(x) \geq 1$ for all $x \in R$
• B

  $f(x)$ is not differentiable at $x=1$
• Correct answer
  C

  $f(x)$ is differentiable everywhere
• D

  $f(x)$ is not differentiable at $x=0$

Solution

$f(x)=\min \{x+1,|x|+1\}$ $f(x)=x+1 \forall x \in R$.

Hence, the correct answer is option: 'C'.