JEE Advance - Mathematics (2009 - Paper 2 Offline - No. 12)
If the function $$f(x) = {x^3} + {e^{x/2}}$$ and $$g(x) = {f^{ - 1}}(x)$$, then the value of $$g'(1)$$ is _________.
Answer
2
Explanation
We have $$f(0) = 1,f'(x) = 3{x^2} + {1 \over 2}{e^{x/2}}$$
$$ \Rightarrow f'(g(x))g'(x) = 1$$
Substituting $$x = 0 \Rightarrow g'(1) = {1 \over {f'(0)}} = 2$$.
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