Practicing Success
Practicing Success
CUET Preparation Today
| 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 |
Discontinuous at $x=2$ Continuous everywhere Differentiable at $x=2$ Discontinuous at $x=1$ |
| Discontinuous at $x=2$ |
| $\lim_{x \to 2+}f(x)=\lim_{x \to 2}2x-3=1$ ,$\lim_{x \to 2-}f(x)=\lim_{x \to 2}2x+3=7$ and $f(2)=7$. Hence $f$ is discontinuous at $x=2$. It is continuous everywhere else. |
