Question

$f\left(x\right)=\{\begin{array}{c}\left[x\right]+[-x],whenx\ne 2\\ \lambda ,whenx=2\end{array}$
If $f\left(x\right)$ is continuous at $x=2$ then, the value of $\lambda$ will be

• A. $-1$
• B. $1$
• C. $0$
• D. $2$

Answer 1

The correct option is A $-1$

Given

$f\left(x\right)=\{\begin{array}{c}\left[x\right]+[-x],whenx\ne 2\\ \lambda ,whenx=2\end{array}$

$LHL=\underset{h\to 0}{lim}[2-h]-[-(2-h\left)\right]$
$=\underset{h\to 0}{lim}1+[-2+h]=1-2=-1$

$RHL=\underset{h\to 0}{lim}[2+h]+[-(2+h\left)\right]$
$=\underset{h\to 0}{lim}2+[-2-h]=2-3=-1$