The point('s) at which the function \( f \) given by \( f(x)=\begin{cases}\displaystyle\frac{|x|}{2x}, & x\lt 0\\ -\displaystyle\frac{1}{2}, & x\ge 0\end{cases} \) is continuous is (are)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( x\in R \): where R is set of all real numbers
For x < 0, \( |x|=-x \), so
\( \displaystyle \frac{|x|}{2x}=\frac{-x}{2x}=-\frac{1}{2} \)
So f(x) = −1/2 for every real x. A constant function is continuous everywhere, so f is continuous at every \( x\in R \).