16.1. Give an example of a bounded and continuous function g on R to R which does not take on either of the numbers sup {g(x):x € R}, inf {g(x) : x € R}.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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demonstrate the exercise in detail (Show each statement that is given)

16.1. Give an example of a bounded and continuous function g on R to R
which does not take on either of the numbers
sup {g(x) :x € R},
inf {g(x):x € R}.
16.J. Show that every polynomial of odd degree and real coefficients has a
real root. Show that the polynomial p(x)
x* + 7x3 – 9 has at least two
real roots.
Transcribed Image Text:16.1. Give an example of a bounded and continuous function g on R to R which does not take on either of the numbers sup {g(x) :x € R}, inf {g(x):x € R}. 16.J. Show that every polynomial of odd degree and real coefficients has a real root. Show that the polynomial p(x) x* + 7x3 – 9 has at least two real roots.
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