In each of the following, the function f(x) is the exponential generating function for the sequence a0, a1, a2, . . . , whereas the function g(x) is the exponential generating function for the sequence b0, b1, b2, . . . . Express g(x) in terms of fix) if
(a) b3 = 3
bn = an, n ∈ N, n ≠ 3
(b) an = 5n, n ∈ N
bn = an, n ∈ N, n ≠ 3
(c) b1 = 2
b2 = 4
bn ∈ N, n ≠ 1, 2
d) b1 = 2
b2=4
b3 = 8
bn = 2an + 3, n ∈ N, n ≠ 1,2,3