Question

The domain of the function y = sin^–1 (– x²) is ______.

Options

• [0, 1]

• (0, 1)

• [–1, 1]

• φ

Answer 1

The domain of the function y = sin^–1 (– x²) is [–1, 1].

Explanation:

y = sin^–1(– x²)

⇒ siny = – x²

i.e. – 1 ≤ – x² ≤ 1 ......(Since – 1 ≤ sin y ≤ 1)

⇒ 1 ≥ x² ≥ – 1

⇒ 0 ≤ x² ≤ 1

⇒ |x| ≤ 1

i.e. – 1 ≤ x ≤ 1