Question

If the function f(x) = sin^-1 (x² – 3), then x belongs to …

(a) [1, -1]

(b) [√2,2]

(c) [-2,-√2] ∪ [√2,2]

(d) [-2,-√2] ∩ [√2,2]

Answer 1

(c) [-2,-√2] ∪ [√2,2]

f(x) = sin^-1 (x² – 3) 

Domain of sin^-1 (x) is [-1, 1] 

⇒ -1 ≤ x² – 3 ≤ 1 ⇒ 2 ≤ x² ≤ 4

⇒ √2 ≤ x ≤ 2 ⇒ √2 ≤ |x| ≤ 2

x ∈ [-2,-√2] ∪ [√2,2]