The domain of the function

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]

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