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JEE MATHEMATICS MCQ: FUNCTIONS

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Let f(x)=sin⁡−1xf\left( x \right) = {\sin ^{ - 1}}x and g(x)=x2−x−22x2−x−6g\left( x \right) = \frac{{{x^2} - x - 2}}{{2{x^2} - x - 6}}. If g(2)=lim⁡x→2g(x)g(2) = \lim\limits_{x \to 2} g(x), then the domain of the function fogfog is
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Correct option: C
(−∞, −2]∪[−43, ∞)( - \infty ,\, - 2] \cup \left[ { - \frac{4}{3},\,\infty } \right)
Option C ((−∞, −2]∪[−43, ∞)(- \infty ,\, - 2] \cup \left[ { - \frac{4}{3},\,\infty } \right)) is correct because it represents the domain where |g(x)| <= 1, ensuring the composite function fog(x) is defined.

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