JEE Main202628 January 2026Morning ShiftMathematicsFunctionsActual

If g(x)=3 x²+2 x-3, f(0)=-3 and 4 g(f(x))=3 x²-32 x+72 , then f(g(2)) is equal to:

Options

A- 7 2
B- 25 6
C7 2
D25 6

Correct answer

C. 7 2

Step-by-step solution

Let f(x) = ax + b . Then 4g(f(x)) = 12(ax+b)^2 + 8(ax+b) - 12 . Comparing with 3x^2 - 32x + 72 : x^2 : 12a^2 = 3 a = 1 2 Constant: 12b^2 + 8b - 12 = 72 3b^2 + 2b - 21 = 0 b = 7 3 or b = -3 . Since f(0) = -3 , b = -3 . x : 8a(3(-3)+1) = -32 -8a = -4 a = 1 2 . So f(x) = x 2 - 3 . g(2) = 3(4) + 4 - 3 = 13 . f(g(2)) = f(13) = 13 2 - 3 = 7 2 .

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