Let p(x) be a real polynomial function in one variable of odd degree and g be a continuous function from ℝ to ℝ. Which of the following statements is always true?

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Mathematics · Real Analysis

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Correct answer

If g is a bounded function, then there exists x0 ∈ ℝ such that p(x0) = g(x0).

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Answer 1

There exists a point x0 ∈ ℝ such that p(x0) = g(x0) for any continuous function g.

Answer 2

If g is a polynomial function, then there always exists x0 ∈ ℝ such that p(x0) = g(x0).

Answer 3

If g is a bounded function, then there exists x0 ∈ ℝ such that p(x0) = g(x0).

Answer 4

There is a unique point x0 ∈ ℝ such that p(x0) = g(x0).

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