jee-main 2014 Q79

jee-main · India · 06apr Composite & Inverse Functions Derivative of an Inverse Function

If $g$ is the inverse of a function $f$ and $f ^ { \prime } ( x ) = \frac { 1 } { 1 + x ^ { 5 } }$, then $g ^ { \prime } ( x )$ is equal to
(1) $\frac { 1 } { 1 + \{ g ( x ) \} ^ { 5 } }$
(2) $1 + \{ g ( x ) \} ^ { 5 }$
(3) $1 + x ^ { 5 }$
(4) $5 x ^ { 4 }$

If $g$ is the inverse of a function $f$ and $f ^ { \prime } ( x ) = \frac { 1 } { 1 + x ^ { 5 } }$, then $g ^ { \prime } ( x )$ is equal to\\
(1) $\frac { 1 } { 1 + \{ g ( x ) \} ^ { 5 } }$\\
(2) $1 + \{ g ( x ) \} ^ { 5 }$\\
(3) $1 + x ^ { 5 }$\\
(4) $5 x ^ { 4 }$

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