Question

Domain of the function defined by `f(x) = 1/sqrt(sin^2 - x) log_10 (cos^-1 x)` is:-

Options

• [0, 1]

• (0, 1]

• [0, 1)

• (0, 1)

Answer 1

(0, 1)

Explanation:

`sin^-1 x > 0` and `cos^-1 x > 0`

Now, `0 < sin^-1 x ≤ pi/2`

⇒ `0 < x ≤ 1` ......(i) and `0 < cos^-1 x ≤ pi`

⇒ `- 1 ≤ x < 1` ......(ii)

Combining (i) and (ii)

0 < x < 1