JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f(x)=\sin ^{-1} x\) and \(g(x)=\frac{x^{2}-x-2}{2 x^{2}-x-6} .\) If \(g(2)=\lim _{x \rightarrow 2} g(x)\), then the domain of the function \(fog\) is .... .
- A \((-\infty,-2] \cup\left[-\frac{3}{2}, \infty\right)\)
- B \((-\infty,-2] \cup[-1, \infty)\)
- C \((-\infty,-2] \cup\left[-\frac{4}{3}, \infty\right)\)
- D \((-\infty,-1] \cup[2, \infty)\)
Answer & Solution
Correct Answer
(C) \((-\infty,-2] \cup\left[-\frac{4}{3}, \infty\right)\)
Step-by-step Solution
Detailed explanation
Domain of \(\operatorname{fog}( x )=\sin ^{-1}( g ( x ))\) \(\Rightarrow \lg ( x ) l \leq 1 \quad, \quad g (2)=\frac{3}{7}\) \(\left|\frac{ x ^{2}- x -2}{2 x ^{2}- x -6}\right| \leq 1\) \(\left|\frac{(x+1)(x-2)}{(2 x+3)(x-2)}\right| \leq 1\) \(\frac{x+1}{2 x+3} \leq 1\) and…
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