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) For A = {1, 2, 3, 4} define functions f and g, such that f is surjective and g is injective. (b) From (a) write down functions fog and go f, and determine whether they are surjective and/or injective. (c) Independently from the choices of (a), prove that function f is surjective if and only if it is inioativo

Q: .

A:

Q: Sketch the graph of a function f that is defined over all real numbers and that is decreasing on the…

A: Given: f(x) is decreasing on the interval -2,3. f(x) is concave down on the interval -2,2 f(x) is…

Q: The following functions all have {1, 2, 3, 4, 5} as both their domain and codomain. For each,…

A:

Q: How do you show the inverse image of the intersecction of S and T equals the intersection of the…

A: To prove : f-1(S∩T)=f-1(S)∩f-1(T) To show f-1(S∩T)=f-1(S)∩f-1(T) need to prove…

Q: Consider the following function: | 4x 9z -19 1 -1 -9z 19 f(2) = 3 13 0 0 0 a) What is the highest…

A:

Q: Define a function f : Q → N of your choice which is surjective. Then prove that the function you…

A:

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

A:

Q: 3. Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, g) E…

A:

Q: elp plssss

A: Statement: Whenever P⇒Q is false then P∧NotQ is true. As it is known that P⇒Q is false only when P…

Q: Let f be the function {(1,4),(2,1),(3,3),(4,2)} and g be the function…

A: Composition of Functions: If and , then the composition of f and g dented by is defined by Note…

Q: A function that is [Select] interval [a, b] has [Select] on a [Select] on that interval.

A: A function that is continuous on a closed interval [a,b] has a maximum and minimum on that interval.…

Q: 20 for x 5 Let f be the function defined above. Which of the following statements is true? A) f is…

A: Here, we are given the following function. Now,          limx→5-f(x)=limx→5-(x2-20)…