Lacey and Richens each have their own personal function machines. Lacey’s machine, $L(x)$, squares the input and then subtracts one. Richens’s function machine, $R(x)$, adds $2$ to the input and then multiplies the result by three.

1. Write the equations that represent $L(x)\ \text{and}\ R(x)$.

   Answer (a):

   $L(x)=x^2−1$

   $R(x)=3(x+2)$

2. Lacey and Richens decide to connect their two machines, so that Lacey’s output becomes Richens’s input. If $3$ is the initial input, what is the eventual output?

   Answer (b):

   $30$

3. What if the order of the machines was changed? Would it change the output? Justify your answer.

   Hint (c):

   Try computing the result for $x=3$ if the order is reversed.