Question

The domain of sin^–1 2x is ______.

Options

• [0, 1]

• [– 1, 1]

• `[-1/2, 1/2]`

• [–2, 2]

Answer 1

The domain of sin^–1 2x is `[-1/2, 1/2]`.

Explanation:

Let sin^–12x = θ

So that 2x = sin θ.

Now – 1 ≤ sin θ ≤ 1

i.e.,– 1 ≤ 2x ≤ 1

Which gives `-1/2 ≤ x ≤ 1/2`.