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MHT CET202616 April 2026Evening ShiftMathematicsFunctionsActual

If f ( x-1 x+1 ) = x + 1 , then f(x) ,dx =

Options

  1. A2 |1 - x| + c
  2. B-2 |1 - x| + c
  3. C2 |1 + x| + c
  4. D-2 |1 + x| + c

Correct answer

B. -2 |1 - x| + c

Step-by-step solution

Let t = x-1 x+1 t(x+1) = x-1 tx + t = x - 1 x(1-t) = t+1 x = t+1 1-t Substituting x in the given equation: f(t) = t+1 1-t + 1 f(t) = t+1+1-t 1-t = 2 1-t Replacing t with x : f(x) = 2 1-x Integrating with respect to x : f(x) ,dx = 2 1-x ,dx f(x) ,dx = -2 |1-x| + c Answer: -2 |1 - x| + c

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