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MHT CET202619 April 2026Evening ShiftMathematicsDifferentiationActual

If f(x) and g(x) are inverse functions of each other and f(x) = x + e^x , then g'(x) = ...

Options

  1. A1 1 + e^ g(x)
  2. Be^ g(x) 1 + e^ g(x)
  3. C1 1 + g(x)
  4. De^ g(x)

Correct answer

A. 1 1 + e^ g(x)

Step-by-step solution

Since f(x) and g(x) are inverse functions of each other, we have f(g(x)) = x . Differentiating both sides with respect to x , we get: f'(g(x)) g'(x) = 1 g'(x) = 1 f'(g(x)) Given f(x) = x + e^x , differentiating with respect to x gives: f'(x) = 1 + e^x Substituting x with g(x) , we get: f'(g(x)) = 1 + e^ g(x) Therefore, g'(x) = 1 1 + e^ g(x) . Answer: 1 1 + e^ g(x)

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