Let Z denote the set of integers. Define function f :Z + Zby f(x) = 5;...

Question

Question

Let Z denote the set of integers. Define function f :Z + Zby f(x) = 5; if x is even and f(x) = x if x is odd. Then f is Selec

science Advanced-Physics

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

A finition f: A B is said to be one-one function if defferent elements of Á have different emages un B Now Gruen - flm] =* Jet y be any unteger in Z C codomain ) Then co-domain f(x)=y 27 x = y l for x = even) & x=y for res old) => x=24 ( for euen a

Add a comment

Answer 2

Similar Homework Help Questions

Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and...

Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and Let R and S be arbitrary nonempty subsets of Z. Define an even indicator function F F: ZP by F(x) = (x + 1) mod 2 for x e Z That is, F(x) 1 if x is even, and F(x) = 0 if x is odd. or neither? Explain. a) Is F: Q P one-to-one, onto, both, or neither? Explain. b) Is F: (Pn...
Let z denote a complete, reflexive and transitive weak preference relation over a set X, and...

Let z denote a complete, reflexive and transitive weak preference relation over a set X, and let > denote the strict preference relations derived from 2. Select one: O a. the strict preference relation is neither transitive nor complete. O b. the strict preference relation is both transitive and complete. c. the strict preference relation is transitive but not necessarily complete. O d. the strict preference relation is complete but not necessarily transitive.
5. Let A = P(R). Define f : R → A by the formula f(x) =...

5. Let A = P(R). Define f : R → A by the formula f(x) = {y E RIy2 < x). (a) Find f(2). (b) Is f injective, surjective, both (bijective), or neither? Z given by f(u)n+l, ifn is even n - 3, if n is odd 6. Consider the function f : Z → Z given by f(n) = (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer

Consider the set of integers Z with the metric da.y)-2supm e Nu (o): 2" divides (r-y)...

Consider the set of integers Z with the metric da.y)-2supm e Nu (o): 2" divides (r-y) (a) Describe the open balls of radius 1 around the centres 0 and 1 (b) Let f : Z -R be defined as f()0 if is even and (x)1 f r is odd. Is f a continuous function from (Z, d) to R equipped with the standard metric? Himt: Use the criterion of continuity in terms of open sets
4) Let D be the set of all finite subsets of positive integers. Define a function...

4) Let D be the set of all finite subsets of positive integers. Define a function (:2 - D as follows: For each positive integer n, f(n) =the set of positive divisors of n. Find the following f (1), f(17) and f(18). Is f one-to-one? Prove or give a counterexample.
Problem 5. Letf: Z+Zbyn -n. Let D, E S Z denote the sets of odd and...

Problem 5. Letf: Z+Zbyn -n. Let D, E S Z denote the sets of odd and even integers, respectively. (a) Prove that fD CE, where D denotes the image of D under f. (b) Is it true that D = E? Prove or disprove. (c) Describe the set f[El. Problem 6. Letf: R R be the function defined by fx) = x2 + 2x + 1. (a) Prove that f is not injective. Find all pairs of real numbers T1,...

(1) Let C[a, b] denote the set of functions that are continuous on (a,b). Define a...

(1) Let C[a, b] denote the set of functions that are continuous on (a,b). Define a function on pairs of function fig E C[a, b] by dı(,9) = /\f(x) – 9(2)| dx. Prove that (C[a,b], du) is a metric space.
Decide whether f is even, odd, or neither f(x)=x4-2x2 + 6 Choose the correct statement O...

Decide whether f is even, odd, or neither f(x)=x4-2x2 + 6 Choose the correct statement O A. The function is even O B. The function is odd. O C. The function is neither even nor odd
1. a) Let A = {2n|n ∈ ℤ} (ie, A is the set of even numbers)...

1. a) Let A = {2n|n ∈ ℤ} (ie, A is the set of even numbers) and define function f: ℝ → {0,1}, where f(x) = XA(x) That is, f is the characteristic function of set A; it maps elements of the domain that are in set A (ie, those that are even integers) to 1 and all other elements of the domain to 0. By demonstrating a counter-example, show that the function f is not injective (not one-to-one). b)...

(b) (3 points) Let p(x) = x + x Show that this function is neither odd...

(b) (3 points) Let p(x) = x + x Show that this function is neither odd nor even Then, show that the function defined by h(x) = P(x) - P(-x)] is an odd function 4. (6 points) (a) (2.5 points) Let f(x) = Vä? - 1 and g(x) = (f)(x) and its domain. . Find the product function

Let Z denote the set of integers. Define function f :Z + Zby f(x) = 5;...

Homework Answers

Add Answer to:
Let Z denote the set of integers. Define function f :Z + Zby f(x) = 5;...

Post as a guest

Earn Coins

Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and...

Let z denote a complete, reflexive and transitive weak preference relation over a set X, and...

5. Let A = P(R). Define f : R → A by the formula f(x) =...

Consider the set of integers Z with the metric da.y)-2supm e Nu (o): 2" divides (r-y)...

4) Let D be the set of all finite subsets of positive integers. Define a function...

Problem 5. Letf: Z+Zbyn -n. Let D, E S Z denote the sets of odd and...

(1) Let C[a, b] denote the set of functions that are continuous on (a,b). Define a...

Decide whether f is even, odd, or neither f(x)=x4-2x2 + 6 Choose the correct statement O...

1. a) Let A = {2n|n ∈ ℤ} (ie, A is the set of even numbers)...

(b) (3 points) Let p(x) = x + x Show that this function is neither odd...

Let Z denote the set of integers. Define function f :Z + Zby f(x) = 5;...

Homework Answers

Add Answer to: Let Z denote the set of integers. Define function f :Z + Zby f(x) = 5;...

Post as a guest

Earn Coins

Add Answer to:
Let Z denote the set of integers. Define function f :Z + Zby f(x) = 5;...