Let’s make understanding function composition easier. Here’s a simpler look at it:

1. Graphing the Functions: First, draw both functions, $f(x)$ and $g(x)$.

   When you find the output of $g(x)$, you then use that result as the input for $f(x)$.

2. Using a Table: You can also use a table to help you see the changes.

   Make a table with three columns: $x$, $g(x)$, and $f(g(x))$.

   This will show how the inputs change when you put them through the functions.

3. A Simple Example: Let’s look at a specific example with two functions:

   • $f(x) = 2x$
   • $g(x) = x + 3$

   Now, let’s find $f(g(2))$:

   • First, calculate $g(2)$. That means $2 + 3$, which equals $5$.
   • Next, we take that result and find $f(5)$.

   So, $f(5) = 2 \cdot 5$, which equals $10$.

4. Understanding the Notation: When you see $f(g(x))$, it means you are first using $g(x)$, and then using that result in $f(x)$.

   It shows the order in which you apply the functions.

By breaking these down into steps, it’s easier to see how function composition works!