Mathematics · Real Analysis
Let p : ℝ → ℝ be a nonconstant polynomial. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The image of a bounded set under p is not necessarily bounded.
- 2Every point x ∈ ℝ has an open neighborhood Ux such that the restriction p|Ux is a homeomorphism onto its image.
- 3The preimage of a connected set under p is a connected set.
- 4The preimage of a compact set under p is a compact set.✓
Correct answer
The preimage of a compact set under p is a compact set.
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