Let $f:R \to R$ be a function defined by $f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$, then which of the following is true?

Question

Let $f:R \to R$ be a function defined by

$f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$, then which of the following is true?

$f(x)$ is differentiale everywhere

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

$f(x) > 1$ for all $x \in R$

$f(x)$ is not differentiable at x = 1

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