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

1.	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» (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]

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»

(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]