AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

The given function is,
f(x)=√‌

x−|x|

x−[x]

Now
x−|x|≥0‌ and ‌x−[x]>0
x>|x|‌ and ‌x>[x]
Therefore, x∈R+−(‌all integers ‌)
Again,
g(x)‌‌=‌

2x

4+x2

y‌‌=‌

2x

4+x2

Rewrite the above equation.
yx2−2x+4y=0
x=‌

2±√4−16y2

2y

From the above equation,
4−16y2≥0 and y≠0
1−4y2≥0 and y≠0
Therefore, y∈[−‌

1

2

,‌

1

2

]−{0}
Range of g(x) is [−‌

1

2

,‌

1

2

]
The D=R+−(‌all integers ‌) and C=[−‌

1

2

,‌

1

2

]
‌ Thus, ‌D∩C=(0,‌

1

2

]