Discuss the continuity of the function `f(x)` given by `f(x)={2-x , x<0`
and `2+x , x>0`
at `x=0`

Answer

The given function is continuous

Explanation

\begin{aligned}
&f(x)= \begin{cases}2-x ; & x<0 \\
2+x ; & x \geq 0\end{cases} \\
&\text { at } x=2 ; \\
&f\left(2^{-}\right)=f(2)=f\left(2^{+}\right) \\
&f\left(2^{-}\right)=4 \\
&f(2)=4 \\
&f\left(2^{+}\right)=4 \\
...