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Limits Continuity and Differentiability question

2021 · 26 Feb · Shift 2 · Q35

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 26 Feb · Shift 2 · Q35

Limits Continuity and Differentiability question

2021 · 26 Feb · Shift 2 · Q35

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f(x) = {\sin ^{ - 1}}x

and

g(x) = {{{x^2} - x - 2} \over {2{x^2} - x - 6}}

. If

g(2) = \mathop {\lim }\limits_{x \to 2} g(x)

, then the domain of the function fog is :

A
$( - \infty , - 2] \cup \left[ { - {4 \over 3},\infty } \right)$
B
$( - \infty , - 2] \cup [ - 1,\infty )$
C
$( - \infty , - 2] \cup \left[ { - {3 \over 2},\infty } \right)$
D
$( - \infty , - 1] \cup [2,\infty )$

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