JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f ( x )=\left[2 x ^{2}+1\right]\) and \(g ( x )=\left\{\begin{array}{ll}2 x -3, & x < 0 \\ 2 x +3, & x \geq 0\end{array}\right.\), where \([t]\) is the greatest integer \(\leq t\) છે. Then, in the open interval \((-1,1)\), the number of points where fog is discontinuous is equal to
- A \(62\)
- B \(60\)
- C \(85\)
- D \(90\)
Answer & Solution
Correct Answer
(A) \(62\)
Step-by-step Solution
Detailed explanation
\(f(g(x))=\left[2 g^{2}(x)\right]+1\) \({\left[2(2 x-3)^{2}\right]+1 ; x<0}\) \({\left[2(2 x+3)^{2}\right]+1 ; x \geq 0}\) \(\therefore\) fog is discontinuous whenever \(2(2 x-3)^{2}\) or \(2(2 x+3)^{2}\) belongs to integer except \(x=0\). \(\therefore 62\) points of…
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