Trigonometric Functions

Let A= \x (0, )- \ 2 \: (2/ )| x|+ (2/ )| x|=2 \ and B= \x 0: x( x-4)-3| x-2|+6=0 \. Then n(A ) is equal to :

1. 4
2. 8
3. 6
4. 2

Answer

(2) 8

Solution

Set A: 2/ | x x|=2 | 2x|= 8 2 0.81

[figure]

The line cuts y=| 2x| at 4 points in (0, ) n(A)=4

Set B: t= x: t2-4t-3|t-2|+6=0 t=0,1,3,4 =\0,1,9,16\

Only x=1 (0, ) and | 2| 0.91 0.81 no common element

(A B)=4+4=8

Answer: (2)