Jeeify
MCQMediumJEE Main 2026 · 22 January, Shift 2Functions

Mathematics Question from JEE Main 2026 · 22 January, Shift 2

Let f(x)=[x]2−[x+3]−3,x∈R,f(x) = [x]^2 - [x+3] - 3,\quad x \in \mathbb{R}, where [ ⋅ ][\,\cdot\,] denotes the greatest integer function. Then

  • A

    f(x)>0f(x) > 0 only for x∈[4,∞)x \in [4,\infty)](streamdown:incomplete-link)

  • B

    f(x)<0f(x) < 0 only for x∈[−1,3)x \in [-1,3)](streamdown:incomplete-link)

  • C

    ∫02f(x) dx=−6\displaystyle \int_{0}^{2} f(x)\,dx = -6

  • D

    f(x)=0f(x) = 0 for finitely many values of xx

Answer & step-by-step solution

Sign in to reveal the correct answer, the full step-by-step solution, and the common mistakes for this question.

Sign in to see the solution

Practice more Functions questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step - free to start.

Start free trialMore on Functions

Related questions