If g(x) is the inverse function of f(x) and f | vedclass

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(A) Given that $g(x)$ is the inverse of $f(x)$,we have $f(g(x)) = x$. Differentiating both sides with respect to $x$ using the chain rule,we get $f^{\

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$1+[g(x)]^4$

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(A) Given that $g(x)$ is the inverse of $f(x)$,we have $f(g(x)) = x$. Differentiating both sides with respect to $x$ using the chain rule,we get $f^{\prime}(g(x)) \cdot g^{\prime}(x) = 1$. We are given $f^{\prime}(x) = \frac{1}{1+x^4}$. Substituting $g(x)$ for $x$ in the expression for $f^{\prime}(x)$,we get $f^{\prime}(g(x)) = \frac{1}{1+[g(x)]^4}$. Substituting this into the differentiated equation: $\frac{1}{1+[g(x)]^4} \cdot g^{\prime}(x) = 1$. Therefore,$g^{\prime}(x) = 1+[g(x)]^4$.

If $g(x)$ is the inverse function of $f(x)$ and $f^{\prime}(x) = \frac{1}{1+x^4}$,then $g^{\prime}(x)$ is

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