Chapter 8.4A, 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 component 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: $\left(1,7\right),\left(2,6\right),\left(6,2\right),\left(\sqrt{5},\sqrt{5}\right)$.

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?