1. Let $ X = \{m, a, t, h\} $, $ Y = \{1, 4, 0\} $, $ Z = \{d, i, s, c, r, e, t, e\} $ (a) Define a function $ f : X \to Y $ that is onto, but not one-to-one. (b) Define a function $ g : X \to Z $ that is one-to-one, but not onto. (c) Define a function $ h : X \to X $ that is neither one-to-one nor onto. (d) Define a function $ k : X \to X $ that is bijective but is not the identity function on $ X $.

Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

1. Let X = {m, a, t, h}, Y = {1,4, 0}, Z = {d,i, s, c, r, e,t, e} (a) Define a function f : X →Y that is onto, but not one-to-one. (b) Define a function g : X → Z that is one-to-one, but not onto. (c) Define a function h : X → X that is neither one-to-one nor onto.

1. Let X = {m, a, t, h}, Y = {1,4, 0}, Z = {d,i, s, c, r, e,t, e} (a) Define a function f : X →Y that is onto, but not one-to-one. (b) Define a function g : X → Z that is one-to-one, but not onto. (c) Define a function h : X → X that is neither one-to-one nor onto.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Suppose that f: A → B is a function, C ≤ B and D C B. Prove that ƒ¯¹(C − D) = ƒ¯¹(C) − ƒ¯¹(D) -

Q: 3. Let f: A → B and g: B → C be functions. Recall that the composition of g and f is the function go…

A: a) To prove that if g and f are injective, then go f is injective, we need to show that for any two…

Q: (d) Given a function F : P({a, b, c}) → Z is defined by F(A) = |A| for all A E P({a,b, c}). i. Is Fa…

A: For the given function F(A)=|A| F will be one one if A=B implies F(A)=F(B) F will be onto if for a…

Q: Let A and B be two sets and f be function. f: A B.Assuming the function f is invertible, what is the…

Q: Provide an example of a that is onto. Can this fun Justify your answer.

Q: Let A, B be sets and f : A → B a function. Let A' CA and B' C B. (a) Prove that f¯¹[ƒ[A']] 2 A'.…

Q: Show that if f is a meromorphic function on C such that C - ƒ(C) has at least three points then f is…

A: Here's how we can prove that if f is a meromorphic function on C such that C'-f(C) has at least…

Q: Let f be the function from {a, b, c} to {1, 2, 3} such that f (a) = 2, f (b) = 3, and f (c) = 1. Is…

Q: 5. Let f: Z → Z be defined by f(n) = n² + 1. (a). Is f a one-to-one function? Explain. (b). Is f an…

A: Given- The function is f(n)=n2+1 and f:ℤ→ℤ. Definition- Let a function from X to Y, One-to-one: If…

Q: Let F(R, R) be the set of all functions from R to R. For any f, g € F(R, R), we define fog € F(R, R)…

A: Given is set of all functions from set of reals to set of reals

Q: Prove the following statement: For any function f : R" - R and any function g : R" R, let h: R" R be…

Q: Let f : {1, 2, 3} → {a, b, c} be one-one and onto function given by f(1) = a, f(2) = b and f(3) =…

A: Consider

Q: A = {2, 3, 4, 5} and B et f : A → B be a func ow. Which of the following

A: A function f: A → B is said to be an ONTO function if, The range that exists for f is the set B…

Q: Let g : B → C and h : B → C be functions. Suppose that go f = hof for every function f: A → B. Prove…

A: We have to prove that g(x) = h(x) for all x belongs to B.

Q: Let D, E be non-empty sets, let ACD, let BCE, and let f: D E be a function. Prove that Anf¹(B) ≤…

Q: Given that f is a function from A onto B, that g :B →C, and that the function g • f is one-one,…

A: In the given question we have to find f and g are one - one function.

Q: Let X = {o, p, s, w}, Y = {a,b, e, g, k}, and Z = {1, 2, 3, 5, 7, 9}. Let ƒ : X → Y where f = {(o,…

A: X=o,p,s,wY=a,b,e,g,kZ=1,2,3,5,7,9f:X→Yf=o,a,p,g,s,e,w,bg:Y→Zg=g,3,e,2,b,9,k,7,a,1

Q: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is not connected but it…

A: No information is given for topology on Y So i have solved only the middle question

Q: Let g : X c R"→ R be a function defined on the finite set X. Does g achieve a maximum and/or a…

Q: Let f: X→Y and g: Y→Z be functions. Prove that if f is an onto function and g∘f is a one-to-one…

Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f: X → Y can be one-to-one or not…

A: By using definition of one-time and onto function we solve the given problem :

Q: (a) Define a function f: N→ N that is one-to-one but not onto. (b) Define a function f: N→ N that is…

Q: Let f be a function, and suppose that A is a subset of the domain of f. The image of A under f is…

A: Let f be a function, and suppose that A is a subset of the domain of f. The image of A under f is…

Q: Let f:X → Y is a function and let {Ba: a e A} be an indexed family of Subset of Y. Show that a)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3,…

Q: Let A={1, 2, 3, 4, 5} and B={a, e, i, o, u}. If ƒ: B → A is a function defined by f ={(a, 4), (u,…

Q: 3. Let A be a finite set. In this exertise functions f, g will be of type g: A→A and f: A → A. (a)…

Q: 3. (a) Let f: X → Y and g: Y→ Z be functions. Prove the following statements. If f and g are both…

A: We can prove the following parts .

Q: The function f is defined as follows: f: R² R² with f(x, y) = (2x, x+y) Which statement is correct?…

Q: Let E = {1, 2, 3} and F = {-2, –1, 0} and define a relation T from E to F as follows: For every (х,…

A: Since you have posted multipart question and we can answer three subparts. So, answering the first…

Q: 12. a. Suppose a function F: X→ Y is one-to-one but not onto. Is F-1 (the inverse relation for F) a…

Q: Let f : X → Y be a function. Define a relation R in X given byR = {(a, b): f(a) = f(b)}. Examine…

A: Given:

Q: Domain of F Co-domain of F X Y F a • d• Domain of G Co-domain of G X Y G a • b e of d• a. Is F…

Question

1. Let $ X = \{m, a, t, h\} $, $ Y = \{1, 4, 0\} $, $ Z = \{d, i, s, c, r, e, t, e\} $

(a) Define a function $ f : X \to Y $ that is onto, but not one-to-one.

(b) Define a function $ g : X \to Z $ that is one-to-one, but not onto.

(c) Define a function $ h : X \to X $ that is neither one-to-one nor onto.

(d) Define a function $ k : X \to X $ that is bijective but is not the identity function on $ X $.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Complexity$

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

Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify your answer.
Let f : A → B be a function. Prove that f is surjective if and only if, for every pair of functions g : B → C and h : B → C, go f = hof : > g = h.
Let f A → B be a function that is one-to-one and onto, and let C be any set such that CCA and f: C → B is still a function. True or False: f: C → B is still one-to-one. True False
1*) Let X = {1,2, 3}, Y = {2,3, 4}, and Z = {1,2}. (a) Define a function f: Z → X that is one-to-one but not onto. (b) Define a function g: X → Z that is onto but not one-to-one. (c) State whether there exists a function h: X →Y that is one-to-one but not onto.
provw it
Let (¥,r) and (¥ ,4) be two topological spaces. Prove that a function f :(X .r)——(¥ ,A) is continuous if and only if the inverse image under / of every A- closed set is a r- closed set.
4 -5 -9 The matrix A = 0 0 -3 has an eigenvalue A = -3. 1 -2 -3
Let f : A → B be a function between sets A and B. Let X1, X2 ⊆ A and Y1, Y2 ⊆ B. a) Prove that if X1 ⊆ X2, then f(X1) ⊆ f(X2). b) Prove that if Y1 ⊆ Y2, then f -1 (Y1) ⊆ f -1(Y2)
3. Let S {1,2, 3, 4} and define functions f,g : S → S by f = {(1,3), (2,2), (3, 4), (4, 1)} and g = {(1, 4), (2, 3), (3, 1), (4, 2)}. Find (a) g-1 o f og (b) f oglog (c) f-1 og –1 -1ofog