Define a function $f:\mathbb{R}\rightarrow \mathbb{R}$ as $f(x)=\begin{cases}2x+3& \text{if}\hspace{.2cm} x \leq 2\\
2x-3,& \text{if}\hspace{.2cm} x>2
\end{cases}$. Then $f$ is
Answer & explanation
Correct answer: option 1
$\lim_{x \to 2+}f(x)=\lim_{x \to 2}2x-3=1$ ,$\lim_{x \to 2-}f(x)=\lim_{x \to 2}2x+3=7$ and $f(2)=7$. Hence $f$ is discontinuous at $x=2$. It is continuous everywhere else.