# Expert Answers

1. Determine whether each of the following functions is 1-to-1 and whether it is onto. Assume the domain and co-domain is Z, the integers. Explain your answers.

1. f(n) = n / 2, assuming integer division

2. g(n) = 4n + 5

2. Given each of the following functions that maps X = {1, 2, 3} to Y = {A, B, C}

f(1) = A, f(2) = B, f(3) = A

g(1) = C, g(2) = B, g(3) = A

Determine whether the function has an inverse. If it has an inverse, provide it. If it does not, explain why not.

3. Refer to the functions in problem 2. What are domain and codomain of both functions? What is the range of each of them?

4. Draw arrow diagrams for both functions defined in problem 2.

5. Given the following two functions f: R → R and g: R → R are defined by the rules:

f(x) = x2 + 10x + 7

g(y) = 5y + 9

Find f ◦ g and g ◦ f.

1. f(n) = n / 2, assuming integer division

2. g(n) = 4n + 5

2. Given each of the following functions that maps X = {1, 2, 3} to Y = {A, B, C}

f(1) = A, f(2) = B, f(3) = A

g(1) = C, g(2) = B, g(3) = A

Determine whether the function has an inverse. If it has an inverse, provide it. If it does not, explain why not.

3. Refer to the functions in problem 2. What are domain and codomain of both functions? What is the range of each of them?

4. Draw arrow diagrams for both functions defined in problem 2.

5. Given the following two functions f: R → R and g: R → R are defined by the rules:

f(x) = x2 + 10x + 7

g(y) = 5y + 9

Find f ◦ g and g ◦ f.

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