Question

In the plot of the function below. Which is the point at which the discontinuity is of removable type?

• A. p
• B. q
• C. r
• D. All the above

Answer 1

The correct option is C

r

Let the function be given by f(x).

The function is said to have a removable discontinuity at $x_0$ provided.

(i) Both $f\left(x_0\right)$ and $\underset{x\to x_0}{lim}f\left(x\right)=L<\infty$ exist.

(ii) $f\left(x_0\right)\ne L.$

The discontinuity is removed by redefining the function as below.

$F\left(x\right)=\{\begin{array}{cc}f\left(x\right)& \text{for x}\ne x_0\\ L& \text{for}x=x_0\end{array}$

This sort of discontinuity is present only at x=r