Let \( S \) be the set of all twice differentiable functions \( f \) from \( \mathbb{R} \) to \( \mathbb{R} \) such that \( \frac{d^{2}f}{dx^{2}}(x)>0 \) for all \( x\in(-1,1) \). For \( f\in S \), let \( X_{f} \) be the number of points \( x\in(-1,1) \) for which \( f(x)=x \). Then which of the following statements is(are) true?
