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MathsJEE Main 4 Apr 2026, Shift 2·Q1·MCQ·Moderate

Sets, Relations & Functions · Inverse of a function

For the function f:[1,∞)→[1,∞)f : [1, \infty) \to [1, \infty) defined by f(x)=(x−1)4+1f(x) = (x-1)^4 + 1, among the two statements:
(I) The set S={x∈[1,∞):f(x)=f−1(x)}S = \{x \in [1, \infty) : f(x) = f^{-1}(x)\} contains exactly two elements, and
(II) The set S={x∈[1,∞):f(x)=f−1(x+1)}S = \{x \in [1, \infty) : f(x) = f^{-1}(x+1)\} is an empty set,
  1. (1)only (I) is TRUE
  2. (2)only (II) is TRUE
  3. (3)both (I) and (II) are TRUE
  4. (4)neither (I) nor (II) is TRUE

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See the full 4 Apr 2026, Shift 2 paper