Inverse Trigonometric Functions
Domain of Inverse Functions
Premium Question
Grade 12
Question:
The domain of $\sin^{-1}(\log_2(x^2/2))$ is:
(1) $(-\sqrt{2}, \sqrt{2})$
(2) $[-2, -1] \cup [1, 2]$
(3) $[-2, 2]$
(4) $(-2, -1) \cup (1, 2)$
Step-by-Step Solution
Key Concept: The argument of $\sin^{-1}$ must satisfy $-1 \leq \log_2(x^2/2) \leq 1$. Convert the log inequalities to bounds on $x^2$ and then on $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)