Question

Discuss the continuity of the function $f\left(x\right)=\left|x\right|+\left|x-1\right|$ in interval $[-1,2]$.

Answer 1

Here, $f\left(x\right)=|x|+|x-1|,x\in [-1,2]$

We, know that modular function is continuous

Hence, $\left(x\right)$ is continuous $\forall x\in R$

& $|x-1|$ is continuous $\forall x\in R$

Thus, sum of $|x|$ & $|x-1|$ is continuous $\forall x\in R$

Thus, $f\left(x\right)$ is continuous $\forall x\in (-1,2)$