5. Let B= {a,b, c}. For each of the following, if possible give an example. If not possible, explain why not. (a) A 1-1 function fi : B → Z (b) An onto function f2: B- z (c) A 1-1 function f3 :Z- B (d) An onto function f4 :Z- B

Q: II. Determine whether the given function is an onto function or no 4. f(x) = 4x-1, for all x ER 5.…

A: A function f from A to B is said to be an onto function if for each b∈B, there exists at least one…

Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

A:

Q: 1. Let f : Z6 → Z6 be such that f(7) = x2 + 3. (a) Is f a well defined function? (b) Is f…

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

Q: Theorem 4. Let X be a set, and let F: X Y be a l-1 and onto function. (a) F-lo F = Idx (b) FoF- =…

A:

Q: Are the following functions 1-1, onto, both, or neither. f: R-R. f(x) = x13 h: Z- Z. h(x) = x g:…

A:

Q: 4. Show that a sublinear functional p satisfies p(0) = 0 and p(-x) ≥-p(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: 2. Consider the following four functions from R into R, determine if onto or 1-1 function. Support…

A: To find out which of the following function is one-one,  onto .

Q: Show that an onto function f :               {1, 2, 3} → {1, 2, 3} is always one-one.

A: Given, f :  {1, 2, 3} → {1, 2, 3}  is an onto function.

Q: Prove that there is a function g(x) that is not everywehre continuous, yet it is even. Prove that…

A: The function f(x) is said to be even if f(x) = f(-x) for all x. The function f(x) is said to be odd…

Q: 1. Let f : Z6 → Z6 be such that f(a) = x2 + 3. (a) Is f a well defined function? (b) Is f…

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

Q: 6. Consider these functions from the set of students in a discrete mathematics class. Under what…

A: (a) The students from the set of student if it is assigned to his/ her mobile number is one to one…

Q: 6. (a) Use the Schröder-Bernstein Theorem to prove that [a, b]| = |(a,b)| for any a, b e R. (b) Use…

A:

Q: Suppose that f(x) is a continuous function on a E-5, 4|, f(-5) = 4, and f(4) = 8. By the…

A: We explain mean value theorem example.

Q: 2. Prove that if f be a nonnegative measurable function on E. Then f = 0 if and only if f =0 a.e. on…

A:

Q: A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the…

A: Relation: Let A  and B  be two sets then relation between A nd B means  the collection of the…

Q: 16.1. Give an example of a bounded and continuous function g on R to R which does not take on either…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: (a) f is a one-to-one function (Type Y for "yes" or N for "no") (b) ƒ is an onto function (Type Y…

A:

Q: 5. Determine whether the function f : Z × Z →Z is onto if a) f (m, n) = m² + n² b)f (m, n) = m³

A: See the solution.

Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f: X → Y can be one-to-one or not…

A: By using definition of one-time and onto function we solve the given problem :

Q: T is a function?

A:

Q: Theorem 1 in Section 2.4 states the following: "If f and g are continuous functions, then f + g is…

A: We have to check given statement is correct or not.

Q: Differential Equestion

A: You have asked a question with multiple sub parts. I will address the first three of them. Please…

Q: 1- DETERMINE A AND BEC FOR THAT THE FUNCTION: (f:C+a=+b -2 +az +b f(=) = IF = #1-i, 2-1+i (f(1– i)…

A: Continuity of complex function:

Q: 2. Let f be a continuous function defined on a closed, bounded interval I = [a, b]. Assume that f is…

A: Intermediate Value Theorem- Let f be a continuous function over a closed interval [a, b] with its…

Q: Give an example of(a) a function f : Z → N that is both one-to-one and onto N; and(b) a function f :…

A: Here, we need to give an example of(a) a function f: Z → N that is both one-to-one and onto N.

Q: A relation R defined on the given set A will satisfy

A:

Q: Let s(x) and c(x) be two functions satisfying s′(x) = c(x) and c′(x) = −s(x) for all x. If s(0) = 0…

A: Given, s′(x) = c(x) and c′(x) = −s(x) for all x. If s(0) = 0 and c(0) = 1, To prove:     [s(x)]2 +…

Q: Suppose we have a function k(t) such that k(7) = 10 and k' (7) = –0.25. %3D

A: b) Assume k(t) = At2 + Bt + C

Q: 7. Find a counterexample or a proof for the following statement: If f: A- B and g : B- C are…

A:

Q: 4. a) Determine if the credit card number 4147180124197779 has a correct check digit. Is this a…

A:

Q: 1. We'll need to establish the Schröder-Bernstein Theorem first. Assume there exists a 1 – 1…

A: Please see below picture for detailed solution.

Q: (2) Determine whether the domain of the following functions is open/closed/neither and bounded or…

A: (a) Given: f(x, y)=2+x+3yDomain of the function: (x,y)|…

Q: 1. Suppose f (x, y, z) is a function of the variables x, y, and z. Each of x = x(t), y = y(t), and…

A: NOTE : As per Bartleby guidelines , in case of multiple questions only first question is answered.…

Q: a. The function f : Z → Z, f(x) = 2x is onto. (A) True (В) False b. The function f : Z → Z, f(x) =…

A:

Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f : X → Y can be one-to-one or not…

A: By using definition of one-time and onto function we solve the given problem :

Q: Which of the following is the statement of Fermat's Theorem? a. If f has a local minimum or maximum…

A:

Q: 7. If a functionf defined in [a, b] is such that o (i) f is derivable in [a, b], (ii) f' (a) and f'…

A:

Q: 22) Lee f be a contioouse function on the closed ineerval [-S,0], where f(-51=0 and rco)=5 which of…

A:

Q: 2.5. Give an example of a bounded function f and an increasing function a defined on [a, b] such…

A:

Q: 7. Modify B(3) to construct a C* function C(2) which satisfies C(2) = 0 if z S 0.. a. b. C(z) = 1 if…

A: please see the next step for solution

Q: 1. Give an example of a function that is one-to-one but not onto. Give an example of a function that…

A: An example of a function that is one to one but not onto b) an function that is not one to one but…

Q: On one side are the two parts of the definition of a function f: X -> Y, the definition of…

A: Definition : A function is an equation for which any x that can be plugged into the equation will…

Q: Show that a one-one function                 f : {1, 2, 3} → {1, 2, 3} must be onto.

A: Given, the function f : {1, 2, 3} → {1, 2, 3} is one-one.

Q: 6. (a) Let ~ be the relation on Mat2(R) defined by: A ~ B if and only if the (2, 1) entry of A – B"…

A: This problem can be solved as follows:

Q: 6 Suppose that a function h satisfies –x² < h(x) < x² for all x. Prove that h is differen- tiable at…

A: Definition used: f'x=limh→0fx+h-fxh and f'a=limh→0fa+h-fah Calculation: Consider the given…

Q: Which of the following function f: R X R → R is not onto?   1 2x - 3   2 3x3 - x   3 x2-2x…

A: The first function is fx=2x-3 which is linear and hence onto The second function is fx=3x3-x solve…

Q: Let g be defined on an interval A, and let c ∈ A. (a) Explain why g'(c) in Definition…

A: Given that function g is gefined on interval A and c∈A

Q: 3 10. Prove the function f : R- {1}- R-{1} defined by f(x) = ()° is bijective. %3D |

A: Given that the function f:ℝ-1→ℝ-1 is defined by fx=x+1x-13