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MHT CET20244 May 2024Morning ShiftMathematicsFunctionsActual

If the function f (x)=x^3+ e ^ x 2 and g (x)= f ⁻¹(x) , then the value of g^ (1) is

Options

  1. A1
  2. B0
  3. C2
  4. D1 2

Correct answer

C. 2

Step-by-step solution

array ll & f (x)=x^3+ e ^ x 2 & f ^ (x)=3 x^2+ e ^ x 2 2 & Given that g (x)= f ⁻¹(x) & gof (x)=x & f (x))=x & Differentiating w.r.t. x, we get & g ^ ( f (x)) f ^ (x)=1 & for x=0, we get & g ^ ( f (0)) f ^ (0)=1 & ~g ^ (1)= 1 f ^ (0) = 1 0+ 1 2 =2 array

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