Area bounded by the min. `{|x|,|y|}=1` and the max. `{|x|,|y|}=2` is

Options

A. 4
B. 8
C. 16
D. 9

Answer

A

Explanation

Min. `{|x|,|y|}=1`
`therefore |x|=1` if `|x|lt |y|`, graph of which is two parallel lines `x=pm1`
excluding for `-1 lt y lt 1`
and `|y|=1` if `|x| gt |y|,` graph of which is two parallel lines
`y=pm1` excluding for `-1 lt xlt1`
Max. `{|x|,|y|}=2`
`therefore |x|-2` if `|x|gt|y|`, graph of which is two parallel lines `x=pm2`
for `-2ltylt2`
and `|y|=2` if `|y|gt|x|`, graph of which is two parallel lines
`y=pm2` for `-2ltxlt2`
Thus, graph of the functions is as shown in the following figure.

As shown in the figure area `=4xx1xx1=4`