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MHT CET202617 April 2026Morning ShiftMathematicsFunctionsActual

If f : R R and g : R R are defined as f(x) = 2x - |x| and g(x) = 2x + |x| , then

Options

  1. A(fog)(2) + (gof)(2) = 0
  2. B(fog)(2) - (gof)(-2) = 0
  3. C(fog)(2) - (fog)(-2) = 0
  4. D(gof)(2) + (gof)(-2) = 0

Correct answer

D. (gof)(2) + (gof)(-2) = 0

Step-by-step solution

Given f(x) = 2x - |x| and g(x) = 2x + |x| . Evaluating the inner functions for the required values: f(2) = 2(2) - |2| = 2 f(-2) = 2(-2) - |-2| = -4 - 2 = -6 g(2) = 2(2) + |2| = 4 + 2 = 6 g(-2) = 2(-2) + |-2| = -4 + 2 = -2 Evaluating the composite functions: (f g)(2) = f(g(2)) = f(6) = 2(6) - |6| = 6 (f g)(-2) = f(g(-2)) = f(-2) = -6 (g f)(2) = g(f(2)) = g(2) = 6 (g f)(-2) = g(f(-2)) = g(-6) = 2(-6) + |-6| = -12 + 6 = -6 Checking the options, for the expression in option (4): (g f)(2) + (g f)(-2) = 6 + (-6) = 0

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