To evaluate the composition of the functions $f(g(x))$ for $x = 0, 1, 2,$ and $3$, we follow the steps below:

Given:

• $f(x) = 2x$ (doubling function),
• $g(x) = x + 4$ (add 4 function),
• Composition $f(g(x)) = f(x + 4)$.

We will evaluate $f(g(x))$ step-by-step for each value of $x$:

1. For $x = 0$:

$g(0) = 0 + 4 = 4$ $f(g(0)) = f(4) = 2 \times 4 = 8$ Thus, $f(g(0)) = 8$.

2. For $x = 1$:

$g(1) = 1 + 4 = 5$ $f(g(1)) = f(5) = 2 \times 5 = 10$ Thus, $f(g(1)) = 10$.

3. For $x = 2$:

$g(2) = 2 + 4 = 6$ $f(g(2)) = f(6) = 2 \times 6 = 12$ Thus, $f(g(2)) = 12$.

4. For $x = 3$:

$g(3) = 3 + 4 = 7$ $f(g(3)) = f(7) = 2 \times 7 = 14$ Thus, $f(g(3)) = 14$.

Summary:

• $f(g(0)) = 8$,
• $f(g(1)) = 10$,
• $f(g(2)) = 12$,
• $f(g(3)) = 14$.

Would you like more details on function composition or have any questions?

Here are 5 related questions:

1. How do you find the composition of two functions in general?
2. What are the domain and range of the composed function $f(g(x))$?
3. How does function composition change if one of the functions is non-linear?
4. Can you explain the significance of the order in function composition?
5. What happens if the range of $g(x)$ is not within the domain of $f(x)$?

Tip: When composing functions, always evaluate the inner function first before applying the outer function.