Search any question & find its solution
Question:
Answered & Verified by Expert
Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{R}$, where $\mathrm{A}=\mathrm{R} \backslash\{0\}$ is such that $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}+|\mathrm{x}|}{\mathrm{x}}$.
On which one of the following sets is $\mathrm{f}(\mathrm{x})$ continuous?
Options:
On which one of the following sets is $\mathrm{f}(\mathrm{x})$ continuous?
Solution:
2151 Upvotes
Verified Answer
The correct answer is:
A
For $x \geq 0$
$f(x)=\frac{x+x}{x}=2$
For $x < 0$
$f(x)=\frac{x-x}{x}=0$
$\lim _{x \rightarrow 0^{+}} f(x)=2$
$\lim _{x \rightarrow 0^{-}} f(x)=0$
$f(0)=2$
$\Rightarrow$ It is discontinuous at $x=0$. Option (a) is correct.
$f(x)=\frac{x+x}{x}=2$
For $x < 0$
$f(x)=\frac{x-x}{x}=0$
$\lim _{x \rightarrow 0^{+}} f(x)=2$
$\lim _{x \rightarrow 0^{-}} f(x)=0$
$f(0)=2$
$\Rightarrow$ It is discontinuous at $x=0$. Option (a) is correct.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.