Question

The number of solutions of the equation $min\{|x|,|x-1|,|x+1|\}=\frac{1}{2}$ is

• A. $0$
• B. $2$
• C. $4$
• D. $6$

Answer 1

The correct option is C $4$

For drawing curve represented by curve, $y=min\{|x|,|x-1|,|x+1|\}$
First plot $y=|x|,y=|x-1|$ and $y=|x+1|$ by a dotted curve as seen from the graph below and then select the lowest curve for each value of $x$ in the dotted curve.
Final graph is shown by bold lines in graph mentioned below



From the graph, it is clear that number as points of intersection of $y=min\{|x|,|x-1|,|x+1|\}$ and $y=\frac{1}{2}$ is $4$