Check the continuity of the function $f$ given by $f(x) = 2x + 3$ at $x = 1$.

Continuous because $\lim\limits_{x \to 1} f(x) = f(1)$.

The correct answer is Option (2) → Continuous because $\lim\limits_{x \to 1} f(x) = f(1)$. ##

First note that the function is defined at the given point $x = 1$ and its value is 5. Then find the limit of the function at $x = 1$. Clearly

$\lim\limits_{x \to 1} f(x) = \lim\limits_{x \to 1} (2x + 3) = 2(1) + 3 = 5$

Thus $\lim\limits_{x \to 1} f(x) = 5 = f(1)$

Hence, $f$ is continuous at $x = 1$.