Question:medium

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.
Updated On: Jul 18, 2026
  • \[ -\frac{f''(0)}{[f'(0)]^3} \]
  • \[ -\frac{f''(a)}{[f'(a)]^3} \]
  • \[ \frac{f''(0)}{[f'(a)]^2} \]
  • \[ -\frac{f''(a)}{[f'(0)]^2} \]
Show Solution

The Correct Option is A

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