Question

The domain of the function $f(x) = \sin^{- 1}\lbrack\log_{2}(x/2)\rbrack$ is

• A. [1, 4]
• B. [– 4, 1]
• C. [– 1, 4]
• D. None of these

Answer 1

Answer: (A)

$1, 4$

Answer 2

$f(x) = \sin^{- 1}\lbrack\log_{2}(x ⥂ / ⥂ 2)\rbrack$

Domain of $\sin^{- 1}x$ is$x \in \lbrack - 1,1\rbrack$

⇒ $- 1 \leq \log_{2}(x/2) \leq 1$ ⇒ $\frac{1}{2} \leq \frac{x}{2} \leq 2$ ⇒ $1 \leq x \leq 4$

∴$x \in \lbrack 1,4\rbrack$.