- Let A = {1, 2, 3, .., 103. Consider f:P(A) → N given by f(B) = |B|. That is, f takes B subset of A to |B|. b. Is f surjective? b. Find f-²(3).

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: Q: Interpret the vate of change f y = (-2 Jn=+1 + 5) (45 -2) with Yespect to

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

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Q: For S in the domain of f, let f ( 5 ) = { f(x): * € S}. Let C and D f de subsets of the domain of f.…

A: S is in the domain of f fS=fx: x∈S Let C and D be subsets of the domain of f Then we have to show…

Q: Consider a ruler that takes as input any integer z and outputs. Is r a function? Why?

A: Given that r takes input as integer z and outputs Here the input is different while the output is…

Q: Suppose f : N → N has the rule f(n) = 4n + 1. i) Determine whether f is 1-1. Justify your answer…

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Q: Define f: [0,21-R by f(x) = x²+2x-1 , then the sup f-inf f is : 1a O (0,2) (0,2) 8.ь о Please choose…

A: Given function is  f(x)= x^2 + 2x -1

Q: oS Let f: A→ B and g : B → A be functions such that gof = 1A- Prove that if g is injective, then f…

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Q: 4. Let X be the set {a, b, c, d, e} and Y be the set{g,h, i,j,k}. A description for the functio f:X…

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Q: Let A = {1,2,3,4, 5, 6} and let f:A → A be given by f(x) ={ 5 fx +1 if x± 6 if x = 6 a. Find f(6),…

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Q: Let g : B → N × N where BCZ given by g(m) = (|m| + 2, |m| + 3). Choose all subsets B such that g is…

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Q: Q. AfX-Y where X,Y € Z* , and 0<X <23 and, 0s Ys59, X is hour of clock and Y is minute of digital…

A: Given: f: X→Y , where X is hour of clock and Y is minute hand of clock It can be clearly observed…

Q: If (f +g) € R[a, b] , then (f.9) € R(a, b] (f - 9) € R[a, b] E R[a, b] none of these

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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.…

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Q: Let g : B → N × N where B C Z given by g(m) = (|m| + 2, |m| + 3). Choose all subsets B such that g…

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Q: d) Let the set A = {1, 2, 3,4} and let P(A) denote the power-set of A. Consider the following…

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Q: Let A = {1,2,3}, B B = = Define the functions f: AC and g: B → C by f(1) = 7, f(2)= 9, f(3) = 7,…

A: We want g o h = f.     So, we want g o h(1) = f(1) = 7            and g o h(3) = f(3) = 7   Now,…

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

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Q: Q1. Let f: X-Y and g: Y - Z be two functions then a. If gof: X-Z bijective function then / and g are…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let ƒ be continuous and nonnegative on [a, b]. Show that there is c € [a, b] with f(c) = (±a få…

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Q: Consider the function f : N → N defined by n? if n is odd f = 2n + 1 if n is even A. Find f(A) if A…

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Q: f. Is the domain of f(x.y)= In (6x + 5y“) bounded or unbounded? O Unbounded O Bounded

A: the domain will be Unbounded because

Q: Q5. Given f(x) = v3x + 5, f: R → R where R is the set of real numbers. а) Find the domain and range…

A: (5) Given function is fx=3x+5 (a) We have to find the domain and range of fx=3x+5. Domain:- The…

Q: (6 pts) Let g: A →→ B and f: BC be two functions. Prove or disprove the followings: (a) if f and g…

A: The objective of this question is to prove or disprove two statements about the composition of two…

Q: 3. Let X = {1,2, 3, 4}, Y = {a, b, c} and let f: XY. Prove by contradic- tion that f can't have an…

A: Given that: X={1,2,3,4}and Y={a, b, c}and f:X→Y

Q: Let A = {1, 2, 3}, B= {4,5,6, 7} If f: A x B → N with f((a, b) = b – a , find the following. a. f…

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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: T F 60. A function f is an injection means that for all a and b in the domain of f, if f(a)=f(b),…

A: According to Bartleby guidelines we can answer only first. Rest please repost

Q: 7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the…

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Q: Determine whether or not f is a function. Justify your answers. 1 a) f: RR where f(x) for every XE R…

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Q: solve this question please : . LetX={1,5,9}andY={3,4,7}.a. Define f: X → Y by specifying that f…

A: a) The function f:X→Y neither one - to - one nor onto  b) The function g:X→Y is one - to one and…

Q: Given x = {5,10,15,20,25,30} and y function from X to Y. Let f(5) = 400, f(10) = 100, f(15) = 500, f…

A: x=5, 10, 15, 20, 25, 30  &amp;  y=100, 200, 300, 400, 500, 600. f5=400,  f10=100,  f15=500,…

Q: Find sets A and B, subsets C and C2 of A, and a function f : A → B so that AC: N C2) c ACi)NAC2). 6.

A: Let A = B = R (set of all real numbers) and let C1 = [-2, 0] and C2 = [0, 2] be subsets of A = R

Q: uestion 6: Suppose f: N N has the rule f(n) = 3n²-1. Determine whether f is 1-1.

A: