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Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let...

Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g = {(c, a), (d, e), (e, e), (f, a), (g, g)}

(a) Consider the composed function g ◦ f.

(i) What is the domain of g ◦ f? What is its codomain?

(ii) Find the function g ◦ f. (Find the set.)

(iii) Is g ◦ f one-to-one? Explain. (iv) Is g ◦ f onto? Explain.

(b) Consider the composed function f ◦ g.

(i) What is the domain of f ◦ g? What is its codomain?

(ii) Find the function f ◦ g. (Find the set.)

(iii) Is f ◦ g one-to-one? Explain.

(iv) Is f ◦ g onto? Explain.

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