What Is written 2

Calculus Level 4

Let \(f(x) \) be a real valued bijective function satisfying \(f'(x) = \sin^2 (\sin (x+1)) \) and \(f(0) = 3 \). Find the value of \(\left( f^{-1}\right)'' (3) \).

Clarifications:

  • \(f'(x) \) denotes the first derivative of \(f(x) \) with respect to \(x\).

  • \(f''(x) \) denotes the second derivative of \(f(x) \) with respect to \(x\).

  • \( f^{-1} (x) \) denotes the inverse function of \(f(x) \).

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