JEE Main202623 January 2026Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f(x)= cases a x²+2 a x+3 4 x²+4 x-3 &, x - 3 2 , 1 2 ~b &, x=- 3 2 , 1 2 cases be continuous at x=- 3 2 . If f f(x)= 7 5 , then x is equal to:

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Correct answer

D. 1

Step-by-step solution

4x^2+4x-3 = (2x+3)(2x-1) . For continuity at x = -3/2 , numerator must vanish there: a(9/4) - 3a + 3 = 0 a = 4 . f(x) = (2x+1)(2x+3) (2x+3)(2x-1) = 2x+1 2x-1 for x -3/2 . f f(x) = f ! ( 2x+1 2x-1 ) = 6x+1 2x+3 . 6x+1 2x+3 = 7 5 30x+5 = 14x+21 x = 1 .

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