Let f:RR be a function defined by f(x)=x+1,|x|+1.

Question

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

Accepted Answer

$$f\left( x \right) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$$

$$ \Rightarrow f\left( x \right) = x + 1\,\forall \,x \in R$$

Hence, $f(x)$ is differentiable everywhere for all $$x \in R.$$

Solutions · 1