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JEE Mains · Maths · STD 12 - 5. continuity and differentiation

ધારો કે  \(f ( x )=\left[2 x ^{2}+1\right]\) અને \(g ( x )=\left\{\begin{array}{ll}2 x -3, & x < 0 \\ 2 x +3, & x \geq 0\end{array}\right.\),જ્યાં \([t]\) એ મહતમ પૂર્ણાંક \(\leq t\). તો વિવૃત અંતરાલ \((-1,1)\) માં, જ્યાં \(fog\) અસતત હોય તેવા બિંદુુોની સંખ્યા ............. છે.

  1. A \(62\)
  2. B \(60\)
  3. C \(85\)
  4. D \(90\)
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Correct Answer

(A) \(62\)

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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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