Question

Following function is continous at the point $x=0$
$f\left(x\right)=\{\begin{array}{c}2x-1,ifx<0\\ 2x+1,ifx\ge 0.\end{array}$

• A. True
• B. False

Answer 1

The correct option is B False

Given

$f\left(x\right)=\{\begin{array}{ccc}2x-1,& & x<0\\ 2x+1& & x\ge 0\end{array}$

$\underset{x\to 0^{-}}{lim}f\left(x\right)=2\left(0\right)-1=-1$

$\underset{x\to 0^{+}}{lim}f\left(x\right)=2\left(0\right)+1=1$

$f\left(0\right)=2\left(0\right)+1=1$

$⟹\underset{x\to 0^{-}}{lim}f\left(x\right)\ne f\left(x\right)=\underset{x\to 2^{+}}{lim}f\left(x\right)$

Hence the function is not continous at $x=0$