Question: Give an example of functions and g, both continuous at x = 0, for which the composite f g is discontinuous at x

Give an example of functions ƒ and g, both continuous at x = 0, for which the composite f _°g is discontinuous at x = 0. Does this contradict Theorem 9? Give reasons for your answer.

Step by Step Solution

★★★★★

3.44 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Yes there exist functions f and g both continuous at x 0 for which the com... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

The Whats Up Moms case tells the story of three friends, Meg Resnikoff, Connie Kin, and Elle Walker, who co-founded a YouTube channel called Whats Up Moms to provide instructive and humorous video...

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...

Give an example of functions f (x) and g(x) such that f (g(x)) is continuous but g(x) has at least one discontinuity.

=Homework: Assignment 2 Question 37, 2.5.66 HW Score: 11.24%, 5.51 of 49 points Part 1 of 2 Points: 0 of 1 Save Give an example of functions f and g, both continuous at x = 0, for which the composite...

Q#2. Give an example of functions f and g , both continuous at x = 0 for which the composite fog is discontinuous at x = 0, Does this contradict Theorem (Composite of Continuous Functions)? Give...

# 7 (chapter 5)(40 points, Due on Friday November 11) Question 1. [3 points each] Use the definition of Limit of functions to prove that x2 2 . 5 5 2 lim x 3 x 1 1 (B) x 1 (A) lim x 0 if x 2 2x (C)...

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Example 18 Prove that the function defined by f x tan x is a continuous function Solution The function f x tan x sin x COS X TU that cos x 0 i e x 2n 1 2 We have just proved that both sine and cosine...

Suppose that and g are discontinuous at x = c. Does it follow that + g is discontinuous at x = c? If not, give a counterexample. Does this contradict Theorem 1(i)? THEOREM 1 Basic Laws of...

4 9 is continuous at x c provided g c 0 Proof We are investigating continuity of f g at x c Clearly it is defined at x c We have 114 lim f g x lim f x g x X C MATHEMATICS Hence f g is continuous at x...

A merger is defined as the combination of two or more firms, in which the resulting firm maintains the identity of one of the firms, usually the larger one. Discuss the motives of Merger? (5: Marks)...

A development has 28 lots that have been in inventory for four years. The market will limit sales to five lots a year. Lot prices will be stable for three years but then increase by 5% per year....

Question 3 Bicksler Corporation has a current ratio of 2 . 0 ca Jaly 2 1 of the curnet year. On July 2 2 . Bickiler purchased ( and received ) mw materials on credit from its surplier. Aveming all...

Statistical Literacy When testing m or the difference of means m1 2m2 from independent populations, how do we decide whether to use the standard normal distribution or a Students t distribution?...

In problem, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages. f(x) = (x - 1) 4 2

In problem, evaluate each expression using the values given in the table. (a) (f ° g)(1) (b) (f ° g)(2) (c) (g ° f)(2) (d) (g ° f)(3) (e) (g ° g)(1) (f) (f ° f)(3) 3 1 -3 -2...

In problem, write a function that meets the given conditions. Fourth-degree polynomial with real coefficients; zeros: -2, 0, 3 + i.

Kristen Lu purchased a used automobile for $13,650 at the beginning of last year and incurred the following operating costs: Depreciation ($13,650 = 5 years) Insurance Garage rent Automobile tax and...

Please record journal entries! 25. June 29: Check # 5012 was used to pay salaries of $985.00 to equipment operators for the week ending June 25. Ignore payroll taxes. 26. June 30: Received a bill for...

Ravsten Company uses a job-order costing system. On January 1, the beginning of the current year, the company's inventory balances were as follows: The company applies overhead cost to jobs on the...