Differentiation

If \(f(x)\) is a differentiable function and \(g(x)\) is a double differentiable function such that \(|f(x)| \leq 1\) and \(f'(x)=g(x)\), where,\(f^{2}(0)+g^{2}(0)=9\) then prove that there exists some \(c \in(-3,3)\) such that \(g(c) \circ g^{n}(c) < 0\).