Think about a function like a machine which converts inputs into outputs. An input number goes into the machine, the machine changes it, and the output emerges. Below, two function “machines” are shown, lined up so that the output from the first function becomes the input for the second function. Now, you will see the composition $f(g(x))\text{,}$ where $g(x) = 3x$ and $f(x) = x^2 - x\text{.}$ Type an input number $x$ into the text box, and press Enter. Then use the slider to show what happens to your input $x$ as the functions are composed.

1. What is $g(2)\text{?}$
   Answer:
2. What is $f\big(g\big(2\big)\big)\text{?}$
   Answer:

The animation shows $f(g(x))\text{.}$ Notice that the function $g(x)$ was used first, because it is inside the parentheses for $f\text{.}$