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MHT CET202616 April 2026Morning ShiftMathematicsFunctionsActual

If f(x) = 4x + 3 6x - 4 , x 2 3 and ( fof )(x) = g(x) where g: R - 2 3 R - 2 3 , then (g ,o ,g ,o ,g ,o ,g ,o ,g) ,(3) =

Options

  1. A3
  2. B1 3
  3. C3^5
  4. D1 3^5

Correct answer

A. 3

Step-by-step solution

Given f(x) = 4x + 3 6x - 4 We find g(x) = (f f)(x) = f(f(x)) g(x) = 4f(x) + 3 6f(x) - 4 Substituting f(x) into the expression: g(x) = 4 ( 4x + 3 6x - 4 ) + 3 6 ( 4x + 3 6x - 4 ) - 4 g(x) = 16x + 12 + 18x - 12 24x + 18 - 24x + 16 g(x) = 34x 34 = x Since g(x) = x , g is the identity function. Any number of compositions of an identity function with itself yields the identity function. (g g g g g)(x) = x Substituting x = 3 : (g g g g g)(3) = 3 Answer: 3

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