Question: 3 — Multiplying and Dividing Functions
LEARNING OBJECTIVE: Multiply or divide two functions.
If $f(x) = 3x^2 - 5$ and $g(x) = -2x + 5$, then $f(3)g(3) = \underline{\hspace{2cm}}$.
a.) 22
b.) 2
c.) -22
d.) -2
1. **State the problem:** We need to find the value of $f(3)g(3)$ given the functions $f(x) = 3x^2 - 5$ and $g(x) = -2x + 5$.
2. **Evaluate $f(3)$:** Substitute $x=3$ into $f(x)$:
$$f(3) = 3(3)^2 - 5 = 3 \times 9 - 5 = 27 - 5 = 22$$
3. **Evaluate $g(3)$:** Substitute $x=3$ into $g(x)$:
$$g(3) = -2(3) + 5 = -6 + 5 = -1$$
4. **Multiply $f(3)$ and $g(3)$:**
$$f(3)g(3) = 22 \times (-1) = -22$$
5. **Final answer:** The value of $f(3)g(3)$ is $-22$.
Therefore, the correct choice is **c.) -22**.