2. Consider the function f : Ro → R: TH x*e-² In |x| and the set U = {x € R, : f(x) > 0}. Which of the following sets is equal to U? (A) The set of real numbers strictly smaller than –1 or strictly greater than 1. (B) The set of real numbers smaller than or equal to –1 or greater than or equal to 1. (C) Th set of real numbers smaller than or equal to –1, equal to 0, or greater than or equal to 1. (D) The set of real numbers strictly greater than 1.

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: Which of the following are true for a function of odd degree with a negative leading coefficient? a)…

A:

Q: 5. Let X be the set of odd integers and Y = {a € Z | a is even and a ≤ 20}, and consider the…

A: (a) Let, f(x) = f(y)          => x(9 – x) = y(9 – y)          => 9x - 9y - x2 + y2 = 0…

Q: 12. For each n € N, define A, = [0, 1+] and B₁ = [0,1]. - =1 (a) Prove that U1A,, is an interval,…

A:

Q: Suppose that f(x) is convex and continuous on an interval I. Show that dif(x1) + ·.+ A„f(xn) + Anf…

A:

Q: 8. Let X and Y be sets, and let C and D be any two sets of Y, and suppose that F: X →Y is a…

A:

Q: 6 language of a function f being continous at a point zo € dom(ƒ). Let f(x) = 2x² +1. Using the e- &…

A:

Q: The functions f and g are defined as f(x) = - 5 , g(x)= X+3' a) Find the domain of f, g, f+g, f-g,…

A:

Q: (5) Consider sets A and B with |A| = sand |B| = t, s≥ t≥1. (a) How many onto functions are there…

A: Sets, A and B with A=s and B=t, s≥t≥1.

Q: 2.58 Given an example of f E C (a, b) for which the range of f is a) a finite open interval. b) an…

A:

Q: Let F be the set of all functions of the form f : N {0, 1}. Also, let G be the set of all functions…

A: We have to find all possible options that are correct for the given question.

Q: How many functions f: {1,2,3,4} {1,2,3,4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b.…

A: Solution :-

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: 1. Give an example of a function f N N which is injective but not surjective.

A:

Q: How many finite functions exist of the form f: {1, 2, 3,...,m} {1, 2, 3,..., n}? How many of them…

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Q: Let X = {1, (b) xm} and Y = {y₁, Yn} be finite sets. Determine the number of one to one functions…

A:

Q: A function f is continuous on [-3, 5] and contains the points (-3, -4), (0, ƒ(0)), and (5, –3). If ƒ…

A:

Q: 6. Let g: X→→ Y and f: Y→ Z be functions. If go f is one-to-one, then f is one-to-one.

A:

Q: 4. Let f and g be functions defined on an open interval I containing the point c. Prove that if f…

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Q: (1) Let f be a function from A to B, {An} a sequence of subsets of A, and {B} a sequence of subsets…

A:

Q: 6. For each of the following, is it a well-defined function? Explain. (a) (b) (d) a: R→Z a(x) = B(n)…

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Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…

A:

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

A:

Q: 3. Let z € R" be denoted by x = (₁, 2,...,n) and || x ||:= √√x² + x² + +x². Let f: RR be defined by…

A:

Q: 5. Prove that if ƒ : [-1, 1] → R is measurable, then |f| is also measurable.

A:

Q: 18. Let A = {1,2, 3}, B = f: A → B, and g : B → C, such that {W, Y, Z}, C = {7, V2, V5}. Find…

A:

Q: How many functions f: {1,2,3,4} → a. ƒ(1) = 1 or ƒ(2) = 2 (or both)? → {1, 2, 3, 4} are there…

A: Since your question carry more than three subparts , so as per Bartleby guidelines we are answering…

Q: Let g: RxR → RxR be a function defined by g(x, y) = (x², x-y). Suppose that X = Rx{0} and D= {(a, a)…

A: Bartleby Guideline : ''Since you have posted a question with multiple sub parts , we will provide…

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)…

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Q: Which of the following relations are functions of y in terms of x? 1) 2) 3) 4) 5- 5+ 5+ 4- 3- 2- 2-…

A:

Q: 13. (9 points) Let D be the set of finite subsets of positive integers. Let S be the set of all…

A: The objective of this question is to find the set of all even factors of given numbers using the…

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: 7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the…

A:

Q: 3. Consider the set X = {a,b,c} and the function f: X→ X defined by the rules f(a) = b. f (b) = a…

A: The set X=a, b, c and the function f:X→X defined by the rules fa=b, fb=a, fc=b. We have to find the…

Q: D. Let function g: R → R be defined by g(x) = 2x + 1 5 cx in its domain. Why does your choice of c…

A:

Q: Determine whether -2, if z < -2 *, if - 22122 |8- z), if 2<z <3 |4 -r, if z 23 f(a) = is continuous…

A: givenf(a)=-2, ifx&lt;-2x5 , if-2≤x≤28-x , if2&lt;x&lt;34-x2 , ifx≥3one limit of this piecewise…

Q: 5. Let f: CC be the function defined by f(2)= 25 for any z € C. Fill in the blanks in the blocks…

A: (I)⇒The function f is surjective(II)⇒Let ζ∈ℂ(III)⇒we have to find some z∈ℂ with f(z)=ζ(IV)⇒and we…