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MathsJEE Main 28 Jan 2026, Shift 2·Q8·MCQ·Easy–moderate

Sets, Relations & Functions · One-one and many-one functions

Given below are two statements :

Statement I : The function f:R→Rf : \mathbb{R} \to \mathbb{R} defined by f(x)=x1+∣x∣f(x) = \dfrac{x}{1 + \lvert x\rvert} is one-one.

Statement II : The function f:R→Rf : \mathbb{R} \to \mathbb{R} defined by f(x)=x2+4x−30x2−8x+18f(x) = \dfrac{x^2 + 4x - 30}{x^2 - 8x + 18} is many-one.

In the light of the above statements, choose the correct answer from the options given below :

  1. (1)Both Statement I and Statement II are false.
  2. (2)Both Statement I and Statement II are true.
  3. (3)Statement I is false but Statement II is true.
  4. (4)Statement I is true but Statement II is false.

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