Question Let f = {(Mindy. Subaru). (Jasmine. Toyota), (Sharon. VW), (Roger, Kia)

Question

Question

Let f = {(Mindy. Subaru). (Jasmine. Toyota), (Sharon. VW), (Roger, Kia)}. What is the domain of this relation? What is the range? Is this a function? Why or why not? Is this relation one-to-one? Why or why not? Define g as {(Mindy, Subaru), (Jasmine, Toyota), (Sharon, VW), (Cindy.VW). (Roger. Kia)}. Is g a one-to-one function? Why or why not? Let f = {(1,2),(2,2),(3,2),(4,2)}. Is this a function? Why or why not? Define f to be a function from R to R by f(x) =x3 + 1. Is f injective? Explain your answer. Is f surjective? Explainyour answer. Give an example of a function f : Z rightarrow Z that is injective but not surjective surjective but not injective bijective neither injective nor surjective. In each case, explain how your example satisfies the given conditions. Define f: R rightarrow R such that f(x)= [x]. This is the ceiling function and assigns to the real number x the smallest integer that is greater than or equal to x. For example [1.2] = 2 because 2 is the smallest integer that is greater than or equal to 1.2. Similarly, we can compute [1] = 1 and [0,9]= 1. Is f one-to-one? Explain. Is f onto? Explain. How would your answer to part (b.) change if we defined the function as follows: f : R rightarrow Z such that f(x)= [x]?

Explanation / Answer

1)

a) domain = {mindy , jasmine, sharon, roger}

b) range = {subaru , toyota , VW ,kia}

c) yes , it is a function because all the elements in domain are such that each element is

mapped to only one element in range

d) every function is a relation

e)no , it is not one-one function as cindy and sharon are mapped to VW (one element)

4)

yes it is a function because elements in the domain {1,2,3,4} are all mapped with only one element i.e ( element 1 is not mapped to two elements in range)

5)

f(x) is injective iff f(x1) = f(x2) => x1 = x2

=>x1^3 = x2^3 = > x1 = x2

a) injective

b)range of function is R all real numbers so every element in range is mapped

so surjective as well

6)

a)this case is not possible

b)f(x) = (x-1)(x-2)(x-3)

c) f(x) = x

d)f(x) = x^2

7)

a) no because [0.8] = [0.9 ] = 1

b)no becuse the return value of function is interger and range R i.e .

[x] cannot be equal to 0.5

c)yes ,now the function is onto

[x] can return all integres

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.