LEFTRIGHTARROW g(y)=x\]                    Now, \[g'(f(x))=\FRAC{1}{f'(x)}\,,\,\forall x\]Þ \[g'(f(x))=1+{{x}^{3}},\ \ \forall x\]            Þ  \[g'(y)=1+{{(g(y))}^{3}}\]           [USING\[f(x)=y\Leftrightarrow x=g(y)]\]                    Þ  \[g'(x)=1+{{(g(x))}^{3}}\]  (replacing y by x).

"> LEFTRIGHTARROW g(y)=x\]                    Now, \[g'(f(x))=\FRAC{1}{f'(x)}\,,\,\forall x\]Þ \[g'(f(x))=1+{{x}^{3}},\ \ \forall x\]            Þ  \[g'(y)=1+{{(g(y))}^{3}}\]           [USING\[f(x)=y\Leftrightarrow x=g(y)]\]                    Þ  \[g'(x)=1+{{(g(x))}^{3}}\]  (replacing y by x).

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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 equal to [Kurukshetra CEE 1996]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) . 10 months ago

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Since \[g(x)\]is the inverse of \[f(x)\], therefore                    \[f(x)=y\]\[\LEFTRIGHTARROW g(y)=x\]                    Now, \[g'(f(x))=\FRAC{1}{f'(x)}\,,\,\forall x\]Þ \[g'(f(x))=1+{{x}^{3}},\ \ \forall x\]            Þ  \[g'(y)=1+{{(g(y))}^{3}}\]           [USING\[f(x)=y\Leftrightarrow x=g(y)]\]                    Þ  \[g'(x)=1+{{(g(x))}^{3}}\]  (replacing y by x).

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Posted on 11 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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