Discrete Mathematics

Consider the sets A = {0, 1, 2, 3, 4} and B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Let f be a function from A to B, whose graph is G(f) = {(0, 0), (1, 2), (2, 4), (3, 6), (4, 8)}

a. If the inverse, f⁻¹, exists, give it as a set of ordered pairs. If it does not exist, say why not.

b. Let g(x)= ⌊ x/2 ⌋ be a function from B to A.

(i) Give the domain of the composition function g ∘ f

(ii) Give the codomain of g ∘ f

(iii) Give g ∘ f as a set of ordered pairs.