Question

the postage charged for first - class mail is a function of its weight. a postal service uses the following table to describe the rates for 2011. complete parts (a)-(e).
weight increment x (oz) first - class postage p(x)
first ounce or fraction of an ounce 41¢
each additional ounce or fraction of an ounce 24¢
c. $p(x)=\begin{cases}41 &\text{if }0 < xleq1\\41 + 24x&\text{if }1 < xleq4end{cases}$
d. $p(x)=\begin{cases}41x&\text{if }0 < xleq1\\41 + 24x&\text{if }1 < xleq4end{cases}$
b) find p(1.3) and explain what it means.
p(1.3)=65. this means that the postage on a 1.3 - oz first - class letter is 65¢.
c) give the domain of p as it is defined above.
(type a compound inequality.)

Explanation:

Step1: Identify domain definition

The function $P(x)$ is defined for weights $x$ starting from greater than 0 ounces. There is no upper - bound mentioned in the problem description but we consider the intervals given in the piece - wise function.

Step2: Write domain inequality

Since the function is defined for $x$ where $0 < x\leq4$ based on the intervals in the piece - wise function for $P(x)$.
$0 < x\leq4$

Answer:

$0 < x\leq4$