Search any question & find its solution
Question:
Answered & Verified by Expert
$$
\text { If } \begin{aligned}
f(x) &=\frac{|x-2|}{x-2}, \quad \text { for } x \neq 2 \\
&=1 \quad, \quad \text { for } x=2,
\end{aligned}
$$
then which of the following statements is true?
Options:
\text { If } \begin{aligned}
f(x) &=\frac{|x-2|}{x-2}, \quad \text { for } x \neq 2 \\
&=1 \quad, \quad \text { for } x=2,
\end{aligned}
$$
then which of the following statements is true?
Solution:
1717 Upvotes
Verified Answer
The correct answer is:
$f(x)$ is discontinuous at $x=2$
Here $\begin{aligned}|x-2| &=x-2, \quad \text { if } x>2 \Rightarrow \lim _{x \rightarrow 2^{-}} f(x)=\lim _{x \rightarrow 2^{+}} f(x)=0 \\ &=-(x-2), \text { if } x < 2 \end{aligned}$
But $f(2)=1 \neq 0$
So $f(x)$ is discontinuous at $x=2$
But $f(2)=1 \neq 0$
So $f(x)$ is discontinuous at $x=2$
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.