Question: User: Unit 2 Lesson 2.1 Assessment
Given the functions $f(x) = 3x + 2$ and $g(x) = x^2 - 5$, determine the value of the following composition of the functions:
$f(f(x))$
$9x+4$
$3x+8$
$9x+8$
$f(f(x))$ does not exist
POSSIBLE POINTS: 2
Graph/shape position_hint: center 6 multiple-choice math question text on a plain page, with no graph visible.
1. **State the problem:** We are given two functions $f(x) = 3x + 2$ and $g(x) = x^2 - 5$. We need to find the composition $f(f(x))$, which means applying $f$ to the result of $f(x)$.
2. **Recall the formula for composition:** The composition $f(f(x))$ means $f$ of $f(x)$, or $f(f(x)) = f\big(3x + 2\big)$.
3. **Substitute $f(x)$ into $f$:** Since $f(x) = 3x + 2$, replace the input $x$ in $f(x)$ with $3x + 2$:
$$f(f(x)) = 3(3x + 2) + 2$$
4. **Simplify the expression:**
$$f(f(x)) = 3 \times 3x + 3 \times 2 + 2 = 9x + 6 + 2$$
$$f(f(x)) = 9x + 8$$
5. **Conclusion:** The value of $f(f(x))$ is $9x + 8$.
Therefore, the correct answer is **$9x + 8$**.