Question

The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.

Options

• [1, 2]

• [–1, 1]

• [0, 1]

• None of these

Answer 1

The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is [1, 2].

Explanation:

Let f(x) = `sin^-1 sqrt(x - 1)`

∵ `sqrt(x - 1) ≥ 0` and `-1 ≤ sqrt(x - 1) ≤ 1`

⇒ 0 ≤ x – 1 ≤ 1

⇒ 1 ≤ x ≤ 2

⇒ `x ∈ [1, 2]`