By the vertical line test, a graph represents a function if no vertical line intersects it more than once. Only the upward-opening parabola (option 3) passes this test; the circle and the sideways-opening curves fail.
Let a ≤ tan^-1 x + cot^-1 x + sin^-1 x ≤ b. If α and β denote the minimum and maximum possible values of a and b respectively, then :
CUET UG 2023 — Mathematics Geometry
2023mcqmedium
Let a≤tan−1x+cot−1x+sin−1x≤b. If α and β denote the minimum and maximum possible values of a and b respectively, then :
Official previous-year question
Held on 30 May 2023 · Verified 13 Jul 2026.
Options
- A
α=0,β=π
- B
α=0,β=2π
- C
α=2π,β=π
- D
α=−2π,β=2π
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