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Let g(x) be the inverse of the function f(x) and f'(x)=\frac{1}{1+x^3} Then g'(x) is :

 

Option: 1

\frac{1}{1+(g(x))^3}


Option: 2

\frac{1}{1+(f(x))^3}


Option: 3

1 + (g(x))3


Option: 4

1 + (f(x))3

 


Answers (1)

best_answer

Since g(x) is the inverse of f(x)

 (gof)(x) = x

  g(f(x)) = x

g'(f(x)) f'(x) = 1


\begin{aligned} & \text { P } \quad g^{\prime}(f(x))=\frac{1}{f^{\prime}(x)}=1+x^3 \\ & \ g^{\prime}(y)=1+(g(y))^2 \\ & {\left[\unrhd=f(x) \ x=f^{-1}(y)=g(y)\right]} \\ & \left.\ g^{\prime}(x)=1+(g(x))^3 \text {. (Replacing y by } x\right) \end{aligned}

Hence (C) is correct answer.

Posted by

Anam Khan

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