VITEEE 2012 Paper

f (x) =

√4−x2

sin−1(2−x)

√4−x2 is defined for 4 - x2 ≥ 0
⇒ x2 ≤ 4
⇒ - 2 ≤ x ≤ 2
and sin−1 (2 - x) is defined for - 1 ≤ 2 - x ≤ 1
⇒ - 3 ≤ - x ≤ - 1
⇒ 1 ≤ x ≤ 3
Also , sin−1 (2 - x) = 0 for x = 2
∴ Domain of f (x) = [- 2 , 2] ∩ [1 , 3] - {2}
= [1 , 2)