Question

The domain of y = cos^–1(x² – 4) is ______.

Options

• [3, 5]

• [0, π]

• `[-sqrt(5), -sqrt(3)] ∩ [-sqrt(5), sqrt(3)]`

• `[-sqrt(5), -sqrt(3)] ∪ [-sqrt(3), sqrt(5)]`

Answer 1

The domain of y = cos^–1(x² – 4) is `[-sqrt(5), -sqrt(3)] ∪ [-sqrt(3), sqrt(5)]`.

Explanation:

y = cos^–1(x² – 4)

⇒ cosy = x² – 4

i.e. – 1 ≤ x² – 4 ≤ 1 ......(Since – 1 ≤ cos y ≤ 1)

⇒ 3 ≤ x² ≤ 5

⇒ `sqrt(3) ≤ |x| ≤ sqrt(5)`

⇒ `x∈ [-sqrt(5), -sqrt(3)] ∪ [-sqrt(3), sqrt(5)]`