If \(f(x)\) is a real valued bijective function and twice differentiable function. If \(g(x)\) is inverse of \(f(x)\) and \(f(0)=a\), then \(g''(a)=\)
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For an inverse function,
\[
\boxed{
(f^{-1})''(y)
=
-\frac{f''(x)}{[f'(x)]^3},
\qquad y=f(x).
}
\]
Always substitute the corresponding value of \(x\) after differentiation.