a. Find the domain. b. Show that at c = 0 the domain has the property described above. c. Evaluate lim, „o f(x). 39. The function f is defined as follows: f(x) = x ifx = 1/n where n is a positive integer, and f(0) = 1. 40. The function f is defined as follows: f(x) = 1 – x if x = 1/n where n is a positive integer, and f(0) = 1. 41. fx) = Vr sin (1/x) 42. f(x) = V In (sin (1/x))

a. Find the domain. b. Show that at c = 0 the domain has the property described above. c. Evaluate lim, „o f(x). 39. The function f is defined as follows: f(x) = x ifx = 1/n where n is a positive integer, and f(0) = 1. 40. The function f is defined as follows: f(x) = 1 – x if x = 1/n where n is a positive integer, and f(0) = 1. 41. fx) = Vr sin (1/x) 42. f(x) = V In (sin (1/x))

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.4: Composition Of Functions

Problem 4SE: How do you find the domain for the composition of two functions, fg ?

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

For the functions in Exercises 39–42,

a. Find the domain.
b. Show that at c = 0 the domain has the property described
above.
c. Evaluate lim, „o f(x).
39. The function f is defined as follows: f(x) = x ifx = 1/n where
n is a positive integer, and f(0) = 1.
40. The function f is defined as follows: f(x) = 1 – x if x = 1/n
where n is a positive integer, and f(0) = 1.
41. fx) = Vr sin (1/x)
42. f(x) = V In (sin (1/x))

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