Let f and g be any two functions, and let M and N be non-negative real numbers. Determine whether each of the following statements is true or false. If true provide a proof. If false, produce a counterexample. (a) If f is M-far from g, then f is M-separated from g. (b) If f is M-separated from g, then f is M-far from g. Before stating the next problem, we need to make some definitions. Let f : R → R and g : R → R be functions, and let M be a positive real number. We define two new relationships that ƒ and g can have. • We say f is M-far from 9 if ExER such that Vy ER, x
Let f and g be any two functions, and let M and N be non-negative real numbers. Determine whether each of the following statements is true or false. If true provide a proof. If false, produce a counterexample. (a) If f is M-far from g, then f is M-separated from g. (b) If f is M-separated from g, then f is M-far from g. Before stating the next problem, we need to make some definitions. Let f : R → R and g : R → R be functions, and let M be a positive real number. We define two new relationships that ƒ and g can have. • We say f is M-far from 9 if ExER such that Vy ER, x
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter67: Analysis Of Trigonometric Functions
Section: Chapter Questions
Problem 18A: For each exercise, functions of two angles are given. Which of the functions of the two angles is...
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Transcribed Image Text:Let f and g be any two functions, and let M and N be non-negative real numbers.
Determine whether each of the following statements is true or false. If true provide a proof. If false,
produce a counterexample.
(a) If f is M-far from g, then f is M-separated from g.
(b) If f is M-separated from g, then f is M-far from g.
Transcribed Image Text:Before stating the next problem, we need to make some definitions. Let f : R → R and g : R → R be
functions, and let M be a positive real number. We define two new relationships that ƒ and g can
have.
• We say f is M-far from
9
if
ExER such that Vy ER, x <y ⇒ |f(y) − g(y)| ≥ M.
• We say f is M-separated from g if
Vx Є R, y = R such that x < y and |f(y) − g(y)| ≥ M.
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