Question

Which of the following statements is/are correct?
1. f(x) is right continuous at x = 0.
2. f(x) is discontinuous at x = 1.
Select the correct answer using the code given below:

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is A 1 only

$f\left(x\right)=\frac{e^x-1}{x}$

$\therefore \underset{x\to 0^{+}}{lim}f\left(x\right)=\underset{x\to 0^{+}}{lim}\frac{e^x-1}{x}=\underset{x\to 0^{+}}{lim}\frac{e^x}{1}=1$

Hence, it is right continuous at $x=0$.

At $x=1$,

$\underset{x\to 1^{+}}{lim}f\left(x\right)=\underset{x\to 1^{+}}{lim}\frac{e^x-1}{x}=e$

$\underset{x\to 1^{-}}{lim}f\left(x\right)=\underset{x\to 1^{-}}{lim}\frac{e^x-1}{x}=e$

Hence, as $LHL=RHL$, the function is continuous at $x=1$