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  4. If the function f(x)=x3+ex / 2 and g(x)=f-1(x), then the value of g prime(1) is

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Q. If the function $f(x)=x^{3}+e^{x / 2}$ and $g(x)=f^{-1}(x)$, then the value of $g^{\prime}(1)$ is

JEE AdvancedJEE Advanced 2009

Solution:

$f(0)=1, f^{\prime}(x)=3 x^{2}+\frac{1}{2} e^{x / 2}$
$\Rightarrow f^{\prime}(g(x)) g^{\prime}(x)=1$
Put $x=0 \Rightarrow g^{\prime}(1)=\frac{1}{f^{\prime}(0)}=2$