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QJEEM22Ma1155: JEE Main 2022 Mathematics - Class 12 JEEM22Ma1155 Solution: Let and g ( x ) = { 2 x − 3 , x < 0 2 x + 3 , x ≥ 0 , where [t] …

Let f(x)=[2x2+1]f(x) = \left[ {2{x^2} + 1} \right] and g(x)={2x−3,x<02x+3,x≥0, where [t] is the greatest integer ≤\le t. Then, in the open interval ( −- 1, 1), the number of points where fog is discontinuous is equal to ______________.

Step-by-Step Verified Solution

f(g(x))=[2 g2(x)]+1\mathrm{f}(\mathrm{g}(\mathrm{x}))=\left[2 \mathrm{~g}^2(\mathrm{x})\right]+1

=\left\{\begin{array}{l}{\left[2(2 x-3)^2\right]+1 ; x&lt;0} \\{\left[2(2 x+3)^2\right]+1 ; x \geq 0}\end{array}\right.

∴\therefore fog is discontinuous whenever 2(2x−3)22(2 x-3)^2 or 2(2x+3)22(2 x+3)^2 belongs to integer except x=0x=0

∴62\therefore 62 points of discontinuity.

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