Question: Let f(x + y) = f(x) + f(y) for all x and y. Prove that there is a number in such that f (t) =

Let f(x + y) = f(x) + f(y) for all x and y. Prove that there is a number in such that f (t) = nit for all rational numbers t.

Step by Step Solution

★★★★★

3.46 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

For any x x 0 x so fx fx 0 fx f0 hence f0 0 Let m be the v... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

955-M-C-D-E (1339).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Let f: X Y be one-to-one and onto. Suppose that f is an open mapping. Then f has a continuous inverse f-1: Y X.

Q:

Let f: X Y be a linear homeomorphism (remark 2.12). Then there exists constants m and M such that for all x1, x2 X, m||x1 - x2|| || f (x1) - f (x2)|| M||x1 - x2||

Q:

Let f be a p.f. for a discrete distribution. Suppose that f (x) = 0 for x [0, 1]. Prove that the variance of this distribution is at most 1/4. Prove that there is a distribution supported on just...

Q:

Let X and Y be sets. Let F: X )Y be some function Let C any subset of Y. Prove that: F(F"(C)) g C The function f: R > R is defined as follows: m+1 :vl for all real numbers 3%1 Determine whether or...

Q:

Section 4.2 The Mean Value Theorem 1. [6 pts]. Verify that the function f satises the hypotheses of the Mean Value Theorem on the given interval. Then nd all number(s) c that satisfy the conclusion...

Q:

Show that log n! is greater than (n log n)/4 for n > 4. Let f (x) and g(x) be functions from the set of real numbers to the set of real numbers. We say that the functions f and g are asymptotic and...

Q:

1) Let f (x) be defined by the function f (x) = x . 3 x2 3 a) Find all critical numbers of f (x) . Show your supporting work

Q:

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...

Q:

CS 70 Discrete Mathematics and Probability Theory Fall 2015 Jean Walrand HW 13 1. Statistical hypothesis testing On one of the Mythbusters episodes1 , the Mythbusters decided to run an experiment to...

Q:

A. Let G be the set of the fifth roots of unity. 1. Use de Moivre's formula to verify that the fifth roots of unity form a group under complex multiplication. Under de Moivre's formula, has five...

Q:

Consider the following situations for Kirkland Welding Services: a. Depreciation for the current year includes equipment, $2,700. b. Each Monday, Kirkland pays employees for the previous weeks work....

Q:

You are hired by the government to evaluate the impact of a policy change that affects one group of individuals but not another. Suppose that before the policy change, members of a group affected by...

Q:

Which of the following could cause a leftward shift of the demand curve for a product? a) increase in income b) decrease in income c) increase in the price of a substitute d) all of the above

Q:

A project with much risk and reward is most likely to be accepted in which of the following? A. An entrepreneurial company B. A heavily regulated company C. A non-profit organization D. A community

Q:

Prove that lim x0 x2 cos (1/x2) = 0.

Q:

(a) For each of the numbers 2, 3, and 4, discover whether is continuous from the left, continuous from the right, or continuous at the number. (b) Sketch the graph of g. 2x- x 2 - x if 0 sI

Q:

Show that the function is continuous on its domain. State the domain. 33. h(x) = xetin. 34. g(x) 6 28 x? - 2

Q:

Suppose Capital One is advertising a 60 -month, 5.86% APR motorcycle loan. If you need to borrow $8,800 to purchase your dream Harley-Davidson, what will be your monthly payment? (Note: Be careful...

Q:

I don't know how to do this Problem: Below is a chart of the current budget for lab salaries. You are assigned the task of preparing a budget proposal for the next fiscal year that represents a 7.5%...

Q:

QSO 321 Module Two Assignment Template\ Complete this template by replacing the bracketed text with the relevant information.\ \\\\table[[Criteria,Canada,[Country Two],[Country Three]],[Authority...