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Mathematics · Functions

JEE Main 2026 — 4 April, Morning Shift — Question 24

Let [·] denote the greatest integer function. If the domain of the function f(x)=cos−1(4x+2[x]3)\mathrm{f(x) = cos^{- 1}\left(\frac{4x + 2[x]}{3}\right)} is [α,β][\alpha ,\beta ] , then 12(α+β)12(\alpha +\beta) is equal to :

  1. Option A:

    6

    Correct
  2. Option B:

    8

  3. Option C:

    9

  4. Option D:

    4

Answer: A

Step-by-step solution

−1≤4×+2[x]3≤1-1 \leq \frac{4 \times+2[\mathrm{x}]}{3} \leq 1 −3−4x≤2[x]≤3−4x-3-4 \mathrm{x} \leq 2[\mathrm{x}] \leq 3-4 \mathrm{x}

x∈[−14,34]12(α+β)=6\begin{aligned} & x \in\left[\frac{-1}{4}, \frac{3}{4}\right] \\& 12(\alpha+\beta)=6 \end{aligned}
Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
4 April, Morning Shift
Subject
Mathematics
Chapter
Functions
Topic
Domain & range of functions

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