Question

Following function is continous at the point $x=2$
$f\left(x\right)=\{\begin{array}{c}1+x,whenx<2\\ 5-x,whenx\ge 2\end{array}$

• A. True
• B. False

Answer 1

The correct option is A True

Given

$f\left(x\right)=\{\begin{array}{ccc}1+x,& & x<2\\ 5-x& & x\ge 2\end{array}$

$\underset{x\to 2^{-}}{lim}f\left(x\right)=1+\left(2\right)=3$

$\underset{x\to 2^{+}}{lim}f\left(x\right)=5-\left(2\right)=3$

$f\left(2\right)=5-2=3$

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

Hence the function is continous at $x=2$