Consider the following statements in respect of a function $f(x)$

I. $f(x)$ is continuous at $x=a$, if $\lim _{x\to a}f(x)$ exists.

II. If $f(x)$ is continuous at a point, then $\frac{1}{f(x)}$ is also continuous at the point.

Which of the above statement(s) is/are correct?

Question

Consider the following statements in respect of a function $f(x)$

I. $f(x)$ is continuous at $x=a$, if $\lim _{x\to a}f(x)$ exists.

II. If $f(x)$ is continuous at a point, then $\frac{1}{f(x)}$ is also continuous at the point.

Which of the above statement(s) is/are correct?

YESPYQ · Accepted Answer

Correct answer: d) Neither I nor II. I. Wrong by definition. II. It's not necessary. For example: $f(x)=x$ is continuous at $x=0$ But $\frac{1}{f(x)}=\frac{1}{x}$ is not continuous at $x=0$.

Consider the following statements in respect of a function \(f(x)\) I. \(f(x)\) is continuous at \(x=a\), if \(\lim _{x\…

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