Question

Following function is continous at $x=0$
$f\left(x\right)=\{\begin{array}{c}x,x>0\\ 1,x=0\\ -x,x<0\end{array}$

• A. True
• B. False

Answer 1

The correct option is B False

Given function is

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

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

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

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

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

So the Function is not continous at $x=0$