Suppose that a function y = f(x) is continuous on I = [a,b] and if the set f(I) = [f(a),f(b)], then y = f(x) is strictly increasing. Is this statement true or false? Why? Please explain with theorems.
Suppose that a function y = f(x) is continuous on I = [a,b] and if the set f(I) = [f(a),f(b)], then y = f(x) is strictly increasing. Is this statement true or false? Why? Please explain with theorems.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 65E
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Suppose that a function y = f(x) is continuous on I = [a,b] and if the set f(I) = [f(a),f(b)], then y = f(x) is strictly increasing.
Is this statement true or false? Why? Please explain with theorems.
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