Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) = − 3x + 2, and h(x) = mx + b. A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (-1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. D. Within the context of the e-8 definition of a limit, your result from part B suggests that if € is equal to 2, the largest that can be chosen for function g(x) is 6. Explain. E. The following statement is (ever so slightly) false: "Within the context of the e-8 definition of a limit, the results from parts B and C suggest that for a given positive real number €, the largest that can be chosen for function h(x) is" Modify this statement (ever so slightly) so that it is true, and

Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) = − 3x + 2, and h(x) = mx + b. A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (-1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. D. Within the context of the e-8 definition of a limit, your result from part B suggests that if € is equal to 2, the largest that can be chosen for function g(x) is 6. Explain. E. The following statement is (ever so slightly) false: "Within the context of the e-8 definition of a limit, the results from parts B and C suggest that for a given positive real number €, the largest that can be chosen for function h(x) is" Modify this statement (ever so slightly) so that it is true, and

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 51E

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