JEE Advanced 2023 Paper 2 Mathematics Q7

Mathematics

Problem

Let S be the set of all twice differentiable functions f from ℝ to ℝ such that d²f/dx²(x) > 0 for all x ∈ (−1, 1). For f ∈ S, let X_f be the number of points x ∈ (−1, 1) for which f(x) = x. Then which of the following statements is(are) true?

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