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MathsJEE Main 28 Jan 2026, Shift 1·Q1·MCQ·Moderate

Sets, Relations & Functions · Composite function equation

If g(x)=3x2+2x−3g(x) = 3x^2 + 2x - 3, f(0)=−3f(0) = -3 and 4g(f(x))=3x2−32x+724g(f(x)) = 3x^2 - 32x + 72, where ff is a differentiable function, then f(g(2))f(g(2)) is equal to:
  1. (1)256\dfrac{25}{6}
  2. (2)−256-\dfrac{25}{6}
  3. (3)72\dfrac{7}{2}
  4. (4)−72-\dfrac{7}{2}
We corrected a printing error in the original paper

Assumption “where ff is a differentiable function” added; the source leaves it unstated, and without it ff may change at x=16/3x = 16/3 to the other root (14−3x)/6(14 - 3x)/6 of the equation, which gives f(13)=−25/6f(13) = -25/6 (option 2).

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See the full 28 Jan 2026, Shift 1 paper