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Domain of an inverse sine or cosine of a rational function

This type of question, asked 5 times: 14 Jun 2022, 29 Jul 2022, 9 Apr 2024, 21 Jan 2026 S1, 24 Jan 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    78
    The domain of the function f(x)=cos⁡−1(x2−5x+6x2−9)log⁡e(x2−3x+2)f(x) =\frac{\cos^{- 1}\left( \frac{x^{2}- 5x+ 6}{x^{2}- 9} \right)}{\log_{e}\left( x^{2}- 3x+ 2 \right)} is

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  2. Question 2

    29 Jul 2022

    169
    The domain of the function f(x)=sin⁡−1(x2−3x+2x2+2x+7)f(x) =\sin^{- 1}\left( \frac{x^{2}- 3x + 2}{x^{2}+ 2x + 7} \right) is :

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  3. Question 3

    9 Apr 2024

    71
    If the domain of the function f(x)=sin⁡−1(x−12x+3)f(x) =\sin^{- 1}\left( \frac{x - 1}{2x + 3} \right) is R−(α,β)R - (\alpha,\beta) then 12αβ12\alpha\beta is equal to:

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  4. Question 4

    21 Jan 2026 S1

    51
    If the domain of the function f(x)=cos⁡−1(2x−511−3x)+sin⁡−1(2x2−3x+1)f(x) =\cos^{- 1}\left( \frac{2x - 5}{11 - 3x} \right)+\sin^{- 1}\left( 2x^{2}- 3x + 1 \right) is the interval [α,β]\lbrack\alpha,\beta\rbrack, then α+2β\alpha + 2\beta is equal to :

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  5. Question 5

    24 Jan 2026 S2

    63
    If the domain of the function f(x)=sin⁡−1(1x2−2x−2)f(x) =\sin^{- 1}\left( \frac{1}{x^{2}- 2x - 2} \right), is (−∞,α]∪[β,γ]∪[δ,∞)( - \infty,\alpha\rbrack \cup \lbrack\beta,\gamma\rbrack \cup \lbrack\delta,\infty), then α+β+γ+δ\alpha + \beta + \gamma + \delta is equal to

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