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Domain of a function built from inverse trigonometric functions

This type of question, asked 6 times: 2021 Paper 19, 2021 Paper 23, 29 Jun 2022, 28 Jul 2022, 10 Apr 2023, 28 Jan 2025. All 6 questions below, oldest first.

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  1. Question 1

    2021 Paper 19

    68
    The domain of the function csc⁡−1(1+xx)\csc^{- 1}\left( \frac{1 + x}{x} \right) is :

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  2. Question 2

    2021 Paper 23

    63
    The domain of the function f(x)=sin⁡−1(3x2+x−1(x−1)2)+cos⁡−1(x−1x+1)f(x) =\sin^{- 1}\left( \frac{3x^{2}+ x - 1}{(x - 1)^{2}} \right)+\cos^{- 1}\left( \frac{x - 1}{x + 1} \right) is:

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  3. Question 3

    29 Jun 2022

    75
    The domain of the function cos⁡−1(2sin⁡−1(14x2−1)π)\cos^{- 1}\left( \frac{2\sin^{- 1}\left( \frac{1}{4x^{2}- 1} \right)}{\pi} \right) is:

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  4. Question 4

    28 Jul 2022

    62
    Considering only the principal values of the inverse trigonometric functions, the domain of the function f(x)=cos⁡−1(x2−4x+2x2+3)f(x) =\cos^{- 1}\left( \frac{x^{2}- 4x + 2}{x^{2}+ 3} \right) is :

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  5. Question 5

    10 Apr 2023

    177
    If the domain of the function f(x)=sec⁡−1(2x5x+3)f(x) =\sec^{- 1}\left( \frac{2x}{5x + 3} \right) is [α,β)∪(γ,δ]\lbrack\alpha,\beta) \cup (\gamma,\delta\rbrack, then ∣3α+10(β+γ)+21δ∣|3\alpha + 10(\beta + \gamma) + 21\delta| is equal to

  6. Question 6

    28 Jan 2025

    140
    Let [x]\lbrack x\rbrack denote the greatest integer less than or equal to x . Then domain of f(x)=sec⁡−1(2[x]+1)f(x) =\sec^{- 1}(2\lbrack x\rbrack + 1) is :

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