Question:
The domain of the function by f(x) = sin-1 √(x – 1) is
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) none of these
Solution:
(a) [1, 2]
We know that, sin-1 x is defined for x ∈ [-1, 1]
So, f(x) = sin-1 √(x – 1) is defined if
0 ≤ √(x – 1) ≤ 1
0 ≤ x – 1 ≤ 1
1 ≤ x ≤ 2
Hence,
x ∈ [1, 2]