Chapter 8.3A, Problem 17A

Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural numbers and the first components is the length of a rectangle and the second is its width. The following machine computes the perimeter (the distance around a figure) of the rectangle. Thus, for a rectangle whose length, $l$, is $3$ and whose width, $w$, is $2$, the input is $\left(3,2\right)$ and the output is $2\cdot 3+2\cdot 2$, or $10$.

a. For each of the following inputs, find the corresponding output $\left(1,7\right),\left(2,6\right)\left(6,2\right)$.

b. Find the set of all the inputs for which the output is $20$.

c. What is the domain and the range of the function?