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Let  \mathrm{g=f^{-1}\: and \: f^{\prime}(x)=\frac{1}{1+x^{4}}\: then \: g^{\prime}(x)}is equal to

 

Option: 1

\left(1+\left(g(x)^{4}\right)^{-1}\right.


Option: 2

\left(1+\left(f(x))^{4}\right)^{-1}\right.


Option: 3

1+(f(x))^{4}


Option: 4

1+(g(x))^{4}


Answers (1)

best_answer

Since  \mathrm{g(f(x))=x so \: g^{\prime}(f(x)) f^{\prime}(x)=1\Rightarrow g^{\prime}(f(x))=1+x^{4}}.

Putting \mathrm{u=f(x)} so that \mathrm{g(u)=x}, we have g^{\prime}(u)

=1+(g(u))^{4}.

Posted by

shivangi.bhatnagar

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