Question

The number of solution(s) of $y=||x{|}^2-2|x|-2|$ and $y=1$ is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C $4$

Given : $y=||x{|}^2-2|x|-2|$
Let us consider curve $y=x^2-2x-2\Rightarrow y=(x-1{)}^2-3$

The graph of $y=x^2$ is


Thus, first shifting $y=x^2$ towards right by $1$ unit and then moving the graph down by $3$ units, we get graph of $y=x^2-2x-2$


Now, graph of $y=|x{|}^2-2|x|-2,$ is


Now, graph of $y=||x{|}^2-2|x|-2|,$ is


As $y=||x{|}^2-2|x|-2|$ and $y=1$ intersects at four distinct points, hence the number of solutions is $4.$