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Domain of a function involving the inverse sine

This type of question, asked 4 times: May 2021 S1, 16 May 2023 S2, 10 May 2024 S2, 13 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    128
    The domain of f(x)=sin⁡−1 ⁣(log⁡2x2)f(x) = \sin^{-1}\!\left(\log_2\frac{x}{2}\right) is

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  2. Question 2

    16 May 2023 S2

    130
    The domain of the function f(x)=sin⁡−1(x−3)9−x2f(x) = \frac{\sin^{-1}(x-3)}{\sqrt{9-x^2}} is

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  3. Question 3

    10 May 2024 S2

    114
    The domain of the function f(x)=sin⁡−1 ⁣(∣x∣+5x2+1)f(x)=\sin^{-1}\!\left(\dfrac{|x|+5}{x^2+1}\right) is (−∞,−a]∪[a,∞)(-\infty,-a]\cup[a,\infty). Then aa is equal to

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  4. Question 4

    13 May 2026 S2

    52
    If f(x)=sin⁡−1[log⁡1/2(x22)]f(x) = \sin^{-1}\left[\log_{1/2}\left(\dfrac{x^2}{2}\right)\right], then the domain of the function f(x)f(x) is:

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