Question

The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.

Options

• 0 ≤ x ≤ 1

• 0 ≤ x ≤ 4

• 1 ≤ x ≤ 4

• 4 ≤ x ≤ 6

Answer 1

The domain of f(x) = `sin^-1 [log_2(x/2)]` is 1 ≤ x ≤ 4.

Explanation:

Given f(x) = `sin^-1 [log_2(x/2)]` 

`\implies -1 ≤ log_2 (x/2) ≤ 1`

`\implies 2^-1 ≤ x/2 ≤ 2^1`

`\implies 1/2 ≤ x/2 ≤ 2`

`\implies` 1 ≤ x ≤ 4