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If g is the inverse of f and f^ (x)= 1 1+x² , then g^ (x) is equal to

Options

  1. A1+[g(x)]²
  2. B-1 1+[g(x)]²
  3. C1 2 (1+x² )
  4. DNone of these

Correct answer

A. 1+[g(x)]²

Step-by-step solution

Given, g= inverse of f=f⁻¹ g(x)=f⁻¹(x) f[g(x)]=x On differentiating w.r.t. x , we get aligned f^ [g(x)] g^ (x) &=1 g^ (x) &= 1 f^ [g(x)] &= 1 1 1+[g(x)]² & g^ (x)=1+[g(x)]² aligned

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