For this question please follow this:Explain in your own words what this problem is asking.Explain the meaning of any notation used in the problem and in your solution.Describe the mathematical concept(s) that appear to be foundational to this problem.Justified solution to or proof of the problem. For the given f:Z → Z, decide whether f is onto and whether it is one-to-one. Prove thatyour decisions are correct.if x is even(2х+ 1,f (x) = } x + 1if x is odd2

Given: f(x)=2x+1, if x is evenx+12, if x is odd Let x and y be the elements of the…

Answered: For the given f:2 → 2, decide whether f…

For the given f:2 → 2, decide whether f is onto and whether it is one-to-one. Prove that your decisions are correct. (2x + 1, f(x) = { x + 1 if x is even if x is odd

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 8E: 8. For the given subsets and of Z, let and determine whether is onto and whether it is...

See similar textbooks

Related questions

Q: Show that f (x) = (x2 + 1) −1 is one-to-one on (−∞, 0], and find a formula for f −1 for this domain…

A: The given function is fx=x2+1-1. This implies that, fb=fab2+1-1=a2+1-1b2+1=a2+1b2=a2b=a on -∞, 0…

Q: Suppose that the function f is defined, for all real numbers, as follows. if x<-2 f(x) =< - (x-1)²+2…

A: The given data in the question is - f(x) = 3 if…

Q: Label each of the following statements as either true or false. Let g: A ------- B and f: B…

A: g: A ------- B and, f: B --------C f 0 g is one-to-one

Q: In this problem you will use Rolle's theorem to determine whether it is possible for the function…

A: f(x)=6x5+5x−17Suppose that f(x) has at least two real roots a and b such that a < b. Since a…

Q: Suppose that the functions and s are defined for all real numbers x as follows. r r(x)=x-6 s(x) =…

Q: If f(1) > 0 and f9) < 0, then there exists a number c between 1 and 9 such that Ac) = 0. く

Q: For each of the following pairs f: Z ------- Z and g: Z --------- Z, decide whether f 0 g is onto or…

A: Consider: fx=4x-3 and gx=1-x. Evaluate f∘g. f∘g=fgx Substitute gx=1-x in place of x in fx.…

Q: Let f(x) = (x – 1)-2 Show that f(0) = f(2) but there is no number c in (0,2) such that f' (c) = 0.…

Q: Let f:R-R be given by f()-3x2-4, Which of the following is true? (A It is onto, but not one-to-one.…

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = 4x- 3 s…

Q: Suppose that the function f is defined, for all real numbers, as follows. 4 if x2 Find f (-2),…

Q: Find the following funtion f(x)=3x^2+2x-2 F(5)

A: The given function is f(x) = 3x2+2x–2 .

Q: Given (a) fo g(x)= (b) go f(x)= (c) go g(x)= (d) fo f(x)= Note: If needed enter as INF and - as…

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x s(x) = 3x²…

A: givenr(x)=x3s(x)=3x2(s-r)(x)=s(x)-r(x)=3x2-x3 answer(s.r)(x)=s(x)r(x)=3x2.x3=3x5 answer

Q: In this problem you will use Rolle's theorem to determine whether it is possible for the function…

Q: Suppose that the functiong is defined, for all real numbers, as follows. +5 if x # 2 4 8 (r) = - if…

Q: Suppose that the function h is defined, for all real numbers, as follows. 1if x#-1 h (x) = - 2 if x…

A: Topic = Function

Q: Suppose that the functions h and g are defined as follows. h (x) =(-1+x)(-4+x) g (x) =-4-5x %3D (a)…

A: Given hx=-1+x-4+xgx=-4-5x To find (a) hg1 (b) All value that are not in the domain of hg

Q: the following statement. 'If yes, explain why. If no, provide a counterexample. For every real…

A: If the function is injective , then the above statement is true.

Q: Suppose that the functions r and S are defined for all real numbers r as follows. r (x) = 4x-3 s (x)…

Q: Suppose that the functionsfand g are defined as follows. S6) =x² +9 2 g(x) = 3x Find the…

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x+6 s…

A: Given : rx = x + 6sx = 4x + 4

Q: In this problem you will use Rolle's theorem to determine whether it is possible for the function…

A: Consider the function

Q: 4x-1 If f (x) = then f is one to one. x2+4'

Q: State the contrapositive and converse (it is not necessary to know what these statements mean). If…

A: Given statement: If f and g are differentiable, then fg is differentiable.

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x)%3D4X-2…

Q: By applying Rolle's theorem, check whether it is possible that the function f(x) = a° + x – 6 has…

Q: Suppose that the functions h and g are defined as follows. h (x) = (x- 6)(x+5) g (x) = -4x+3 (a)…

Q: Suppose that the functions g and h are defined as follows. g (x) = 4 – 3x? h (x) =7-8x (2) Find (4).…

A: Given, g(x)=4-3x2, h(x)=7-8x

Q: Suppose that the functionh is defined, for all real numbers, as follows. +5 if x -1 h (x) =' if x=-1…

Q: Determine if the following statement is True/False: For every f(n), g(n) such that f(n) ∈ O(g(n)),…

Q: Suppose that the function f is defined, for all real numbers, as follows. x+1 if x<-1 S) = -(x+1…

Q: Which of the following correctly describes the end behavior of f(x) = -x* +2x ? O A. As X → - 0,…

A: Given:- Function f(x)=-x4+2x

Q: For the given f: Z------Z, decide whether f is onto and whether it is one-to-one. Prove that your…

A: One One function A function is said to be one one if and only if there exit a distinct image of a…

Q: In this Discre te math problem youmust prove /dis. Surgective. f= 9X+2

A: Dear student Below In the image is solution of your problem

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=4x-5…

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x)= 3x-2 t(x)=…

A: The given function is: sx=3x-2tx=x-6 To write the expression for: t+sxt×sx To evaluate the value…

Q: Suppose that the functions h and g are defined as follows. h (x)= (x– 5)(x+3) g (x)=6x+1 (a) Find…

A: Given that h(x)= (x-5)(x+3) and g(x)=6x+1. We find h/g (x) and also find the value that are not in…

Q: Suppose that f(x) = x*, x 2 5, and that g(x) = Vx + 3, x > 5. Find a formula for (f • g)(x) and find…

A: fx=x4, x≥5 & gx=x+3, x≥5 Now, f∘gx=fgx=fx+3=x+34=x+32

Q: Suppose that the functions g and h are defined as follows. g (x) =x+4 h (x) = (x+5)(x-5) %3D (a)…

Q: In this problem you will use Rolle's theorem to determine whether it is possible för the function…

Q: In each of the following cases, state whether the function is one-one, onto or bijective. Justify…

A: Given:

Q: Suppose that the function /i is defined, for all real numbers, as follows. 2 ifx+-2 h (x) = -2 if…

A: Given function is: hx=14x-2if x≠-2-2if x=-2 To find: h-5, h-2 and h0. Solution: If x=-5 then…

Q: For the given f: Z------Z, decide whether f is onto and whether it is one-to-one. Prove that your…

A: Given : f : Z → Z defined by f(x) = 2x - 1if x is even2xif x is odd To…

Q: Consider the following statements regarding the function f(x) = 3- x + In x = 0. Statement I: One of…

Q: a) Prove or disprove: f: Z3 → Z5, (r]3+ [r*]5 is well defined.

Q: Consider the function f : N → N given by the formula f(n) = 2n. Is f one-to-one? Explain your…

Q: Suppose that the function f is defined, for all real numbers, as follows. 1 if x 2

Q: Suppose that the functions h and g are defined as follows. h (x) = (3+x)(-4+x) g (x) = 1-7x (a) Find…

A: Given functions h(x)= (3+x)(-4+x) g(x) = 1-7x

Question

For this question please follow this:

Explain in your own words what this problem is asking.
Explain the meaning of any notation used in the problem and in your solution.
Describe the mathematical concept(s) that appear to be foundational to this problem.
Justified solution to or proof of the problem.

For the given f:Z → Z, decide whether f is onto and whether it is one-to-one. Prove that
your decisions are correct.
if x is even
(2х+ 1,
f (x) = } x + 1
if x is odd
2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions are correct. a. f(x)={ x2ifxiseven0ifxisodd b. f(x)={ 0ifxiseven2xifxisodd c. f(x)={ 2x+1ifxisevenx+12ifxisodd d. f(x)={ x2ifxisevenx32ifxisodd e. f(x)={ 3xifxiseven2xifxisodd f. f(x)={ 2x1ifxiseven2xifxisodd
4. Let , where is nonempty. Prove that a has left inverse if and only if for every subset of .
Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove that f is one-to-one. Prove that f is onto if and only if a=1 or a=1.
Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.
For each of the following parts, give an example of a mapping from E to E that satisfies the given conditions. a. one-to-one and onto b. one-to-one and not onto c. onto and not one-to-one d. not one-to-one and not onto
27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .
Prove that if f is a permutation on A, then (f1)1=f.
8. For the given subsets and of Z, let and determine whether is onto and whether it is one-to-one. Justify all negative answers. a. b.
For each of the following mappings f:ZZ, determine whether the mapping is onto and whether it is one-to-one. Justify all negative answers. a. f(x)=2x b. f(x)=3x c. f(x)=x+3 d. f(x)=x3 e. f(x)=|x| f. f(x)=x|x| g. f(x)={xifxiseven2x1ifxisodd h. f(x)={xifxisevenx1ifxisodd i. f(x)={xifxisevenx12ifxisodd j. f(x)={x1ifxiseven2xifxisodd