Question

The area of the region bounded by $y=|x-1|$ and $y=3-\left|x\right|$ is:

• A. less than $5$
• B. greater than $3$
• C. greater than or equal to $4$
• D. less than or equal to $4$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A less than $5$
B greater than or equal to $4$
C less than or equal to $4$
D greater than $3$

$y=|x-1|=\left\{\begin{array}{cc}1-x& x<1\\ x-1& x\ge 1\end{array}\right\}$
Similarly $y=3-|x|=\left\{\begin{array}{cc}3+x& x<0\\ 3-x& x\ge 0\end{array}\right\}$
The required region is a rectangle with length $2\sqrt{2}$ and breadth $\sqrt{2}$.
Hence, the area is 4. Hence, all the options are correct