Let X be a set and XX the set of all functions from X into X. Show that function composition on X is associative on XX. Then prove or disprove if the composition of injective functions is injective.

Q: Give an example of a function that is one-to-one but not onto. Give an example of a function that is…

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Q: Let f, g be two functions from a set A to itself. If f o g is surjective, does it imply that g o f…

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Q: g(x) = e2" + x² – 2 with R>0 - 2²

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Q: Write out all functions f: {1,2} {a, b, c, d) (in two-line notation). How many functions are there?…

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Q: If A and B are finite, show that the set of all functions f: A B is finite.

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Q: How do you show the image of the intersecction of S and T is a subset of the intersection of the…

A: Let function f from A into B. Let S and T are subset of A. To show that fA∩B⊂fA∩fB. Let y∈fA∩B. To…

Q: Let ℝ+ denote the set of positive real numbers. Define a relation E on ℝ+ as follows: a E b  if and…

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Q: Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A…

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

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Q: If f is a function having as its domain and range the set N of natural numbers, then f is bijective.

A: For the solution follow the next step.

Q: True or False A function is a relation between two sets Dand R so that each element x in the first…

A: By definition: A function is a relation from a set of inputs to a set of possible outputs where each…

Q: Determine whether the function f from { a, b, c, d} to { a, b, c, d} is injective (one - to - one),…

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Q: Suppose that the relation R is reflexive. Show that R* is reflexive.

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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  &  y=100, 200, 300, 400, 500, 600. f5=400,  f10=100,  f15=500,…

Q: f(x,y)=x² + 3y + 7. R is he region shown in Fig. 5 (include the boundary). y =2-x y-4- R Fig. 5

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Q: Let f = {(1, 2), (3, 4), (2, 6), (5, 9}. Find the domain of f

A: Given function  f = { ( 1 , 2 ) , ( 3 , 4 ) , ( 2 , 6 ) , ( 5 , 9 ) }

Q: f (x,y)= y² -2x² +10. Ris the region bounded by the parabola y = x and the line y = 4.

A: According to the given information, it is required to find the maximum and minimum value of f on the…

Q: Let A = {1, 2} and B = {-1,0, 1}. Answer the following questions using careful, accurate notation…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.