JEE Main 2026 Mathematics question
For the function f : [1, ∞) → [1, ∞) defined by f(x) = (x−1)⁴ + 1, among the two statements: (I) The set S = {x ∈ [1, ∞) : f(x) = f⁻¹(x)} contains exactly two elements, and (II) The set S = {x ∈ [1, ∞) : f(x) = f⁻¹(x+1)} is an empty set,
Answer: (A)
Solution
f is strictly increasing, so f(x) = f⁻¹(x) forces f(f(x)) = x, whose only solutions for a strictly increasing function are fixed points f(x) = x: (x−1)⁴ = x−1 gives x = 1, 2
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