The point of discontinuity of the function

$f (x) =$ ${\begin{matrix} 2 x + 3, & if x \leq 2 \\ 2 x - 3, & if x > 2 \end{matrix}$ is:

Question

The point of discontinuity of the function

$f (x) =$ ${\begin{matrix} 2 x + 3, & if x \leq 2 \\ 2 x - 3, & if x > 2 \end{matrix}$ is:

Smart Achievers · Accepted Answer

(3)

Ans. $x = 2$

Explanation:

$\lim_{x \to 2^{-}} f (x) = 2 (2) + 3 = 7$ and $\lim_{x \to 2^{+}} f (x) = 2 (2) - 3 = 1$

$∴$ $\lim_{x \to 2^{-}} f (x) \neq \lim_{x \to 2^{+}} f (x)$

Hence, the function is discontinuous at $x = 2$

Want Us to Email you About Special Offers & Updates?