8. Let the functions f: A → B, g:B → C,h: C → D be defined by the figure below. A B h D 3 a. Which function is one-to-one (injective)? Explain. b. Which function is onto (surjective)? Explain.

Q: 6. Determine the type of the following functions ( Injection, Surjection, Bijection?). a) Let f be…

A: The solution given as,   a:-  Let 'f' be the function from             a,b,c,d to1,2,3      and…

Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

A:

Q: 3. Let f be a function from X into Y. Suppose A and B are subsets of X. Prove that f(A U B) = f(A) U…

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Q: Let f:N→Z be the function defined by f(n) = n + 3. Then f is surjective. True False

A: Given that : Let f : N->Z be the function defined by f(n) = n+3 A function basically said to be…

Q: Determine the domain of the function. h(z) = (z − 8)11 + (z − 9)−11

A:

Q: 36. Let f be a twice-differentiable function of z such that, when z = c, f is increasing, concave…

A: We have given function of x which is twice-differentiable such that when x=c, f is increasing,…

Q: 2. Determine whether f is a function from Z to R if a) f(n) =±n. b) f(n) = Vn²+1. c) f(n) = 1/(n² –…

A:

Q: 6.42. Describe the sets in which the functions below are positive. (a) f(x,y) = 1-x?

A:

Q: 15. Determine whether the function f: Z x Z Z is onto if a) f(m, n) =m+n. b) f(m, n) = m² + n². c)…

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

Q: Consider sets A and B with |A|=8 and |B|=5. How many functions f: A→B are surjective?

A: Given: The number of elements in the set A is 8 and the number of elements in the set B is 5.

Q: P @Preve that a)fog is ene to ene Brove thal O (fogl' 6)=Glof)() ouf: Let f amd a be one-to-ene…

A: Let f:A→B and g:C→A be one-to-one function. (a) To prove: f∘g:C→B is one-to-one Let x and y be any…

Q: Prove or provide a counterexample to the following statement: if f : A → B and g : B → C are…

A:

Q: (a) What does it mean if a function f: A B is not surjective?

A:

Q: Determine whether the function f : Z × Z → Z is onto if a) f (m, n) = m + n. b) f (m, n) = m2 + n2.…

A:

Q: Let f : R" → R be a function. Consider the converse proposition of (6.1) given below: If La(f) is a…

A: Consider the converse proposition of (6.1) given below: if ℒα(f) is convex set for each α∈ℝ, then f…

Q: 5. Let f(x,y) = x² + xy + y² be a function on the domain D = {(x,y) R²: x + y ≤8 and y ≥ 9}. a) Why…

A: Given fx, y=x2+xy+y2 Domain D=x, y∈R2; x4+y4≤8 and y≥9

Q: 1. Use (11.20) to check whether the following functions are concave, convex, strictly con- cave,…

A: TO FIND: Whether the functions are concave, covex, stictly convex or neither?

Q: 19. Suppose f :X Y is a function. Which of the following are possible? Explain. a. fis injective but…

A:

Q: Give a proof of the following statement. Suppose A, B and C are sets, f is a surjective function…

A:

Q: 5. Let f(x,y) = x² + xy + y² be a function on the domain D = {(x,y) € R²: 24+ y ≤8 and y ≥ 9}. a)…

A: a) Given that fx,y=x2+xy+y2 First, find critical points. fx=2x+yfy=x+2y So,…

Q: Which of the following are functions from.16 ?the set of real numbers to itself fi = ((1,x): x E R)…

A: Given: The relations from set of real numbers to itself as f1=1,x : x∈Rf2=x3,x : x,y∈Rf3=x,x :…

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: 1. Define function f : Z+ → Z such that f(n) = /n. (a) Is f one-to-one? Justify (prove) your answer.

A:

Q: Define a function S : Z+ → Z+  as follows. For each positive integer n, S(n) = the sum of the…

A: Define a function S : Z+ → Z+  as follows. For each positive integer n, S(n) = the sum of the…

Q: Prove or disprove. The function f(2) = 2z – 3 – ze? + e=% is not entire.

A:

Q: 5. In the table, indicate if the expression is: 1) a function, 2) onto, 3) one-to-one, and 4)…

A: To find: First column of given table is: A function, onto, one-to-one and bijective.

Q: [a, b]as: Let f (x) be a function defined on handwriting 1 :x € Qn [a, b] f(x) = :x € Qn [a, b]…

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Q: Determine if each function is injective, surjective or bijective. Give one counterexample for each…

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Q: Let A- (Blanche, Rose, Sophia, Dorothy), B-(Red, Blue, Yellow) and consider the function f: A B…

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Q: Consider sets A and B with |A| = 8 and |B| = 21. %3D a. How many functions f: A → B are there? b.…

A:

Q: 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?…

A: Let f be the subset of Z × Z defined by  f = {(ab, a + b) : a, b ∈ Z}. We observe that  That is the…

Q: Consider sets A and B with |A| = 12 and |B|| 8. How many functions f : A → B are surjective?

A: We will find out the required value.

Q: ?Determine whether each of these functions from {a, b, c, d} to itself are onto a) f (a) = b, f (b)…

A: For any function to be onto, there are no elements in the co-domain that do not have a pre image.

Q: Let f : A → B be a function. Prove that if C C A and D C A and f is injective, then f(C) = 7 (D) =→…

A:

Q: If the following arrow diagram defines a function f, then the pre-image of 4 is A B f. A +B 1 3 9 4…

A: Given ,  This arrow diagram defines a function f , then  We have to find the pre - image of 4

Q: 4) Consider the function g(x) = [2r – 1] where g : R → Z. a) Is g a one-to-one function? Explain. b)…

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Q: Consider functions f : [5] → [9] (a) How many of the functions are injective

A: Given :  f :5→9  Calculate : Number of injective functions.

Q: c) Does the equality |A U B| = |A| + |B| hold for some sets A and B? d) Is the composition of two…

A:

Q: Let f : S → T be a function, and let A and B be subsets of T. Prove or give a counterexample to the…

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Q: Let X, Y be nonempty sets. Let A, B c X and P, Q C Y. Let f:X → Y be a function. Prove or give…

A:

Q: Consider a function f : N x N-→ N given by f(æ, y) = 37. For what natural n, 21 · 57 is in the image…

A:

Q: (a) Let f: [a, b] - Show that fE R([a, b)). R be abounded monotonic deczeasing function.

A:

Q: Consider functions f:{1,2,3,4} → {a, b, c}. a. How many functions are there? b. How many functions…

A:

Q: 3. In each part, find a function f : N → N that has the desired properties. (i) Surjective, but not…

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

Q: b. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. i. f(a) = b,…

A: We are entitled to solve only one question at a time so, I am providing you the answer of first…

Q: f(x,y) = x2 − y from Z × Z → Z. Is this function injective, bijective, surjective, or none of the…

A: The given functions are to be checked for into and onto

Q: Consider the rule f which maps elements in the set A into the set B and which is illustrated below.…

A:

Q: 5. Determine whether f is a function from Z to R if a) f (n) = ±n. b) f (n) = v n2 + 1. c) f (n) =…

A:

Q: What is the domain of the function f(x) = VIn a ? %3D O le, 00) O 0, 7) O [1, 00) O -0, 00) O ( 0,…

A:

Q: 2. Let X, Y and Z be sets. A, B are subsets of X. f:X → Y is a function. Prove the given statement…

A: