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

Question

Let $f: R \rightarrow R$ be a function defined by $f(x)=\min \{x+1,|x|+1\}$, Then which of the following is true?, $f(x)$ is differentiable everywhere, $f(x)$ is not differentiable at $x=0$, $f(x) \geq 1$ for all $x \in R$, $f(x)$ is not differentiable at $x=1$

MARKS App · Accepted Answer

$\begin{aligned} & f(x)=\min \{x+1,|x|+1\} \Rightarrow f(x) \ & =x+1 \forall x \in R \end{aligned}$ Hence, $f(x)$ is differentiable everywhere for all $x$ $\in R$

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