44. Let $C = \{p, n, d, q\}$, where p, n, d, and q stand for penny, nickel, dime, and quarter, respectively (as in the previous assignment). Define a function as follows:
$f: C \to \mathbb{Z}$
$f(x) = $ the value (in cents) of coin x
Find each of the following.
a. f(d)
b. the codomain of f
c. the range of f
45. Let $C = \{p, n, d, q\}$ as in the previous problem, and define a function as follows (where $P(C)$ denotes the power set of C).
$g: P(C) \to \mathbb{Z}$
$g(S) = $ the total value (in cents) of the coins in S
(Note that for this function, the domain consists of the elements of $P(C)$, i.e. the subsets of C. For instance, $g(\{n, q\}) = 30$.)
Find each of the following.
a. The image of $\{p, n, d\}$ under g
b. The inverse image of 36 under g
