Question: 2 — Adding and Subtracting Functions
LEARNING OBJECTIVE: Add or subtract two functions.
If $f(x) = 2x^2 + 3x - 1$ and $g(x) = -x$, then $f(-1) + g(-1) = \underline{\hspace{2cm}}$.
a.) -1
b.) -3
c.) 1
d.) -5
1. **State the problem:** We need to find the value of $f(-1) + g(-1)$ given the functions $f(x) = 2x^2 + 3x - 1$ and $g(x) = -x$.
2. **Recall the formula:** To find $f(a)$ for some value $a$, substitute $x = a$ into the function $f(x)$. Similarly for $g(a)$.
3. **Calculate $f(-1)$:**
$$f(-1) = 2(-1)^2 + 3(-1) - 1 = 2(1) - 3 - 1 = 2 - 3 - 1$$
Simplify:
$$2 - 3 - 1 = (2 - 3) - 1 = -1 - 1 = -2$$
4. **Calculate $g(-1)$:**
$$g(-1) = -(-1) = 1$$
5. **Add the results:**
$$f(-1) + g(-1) = -2 + 1$$
Simplify:
$$-2 + 1 = -1$$
6. **Final answer:**
$$f(-1) + g(-1) = -1$$
Therefore, the correct choice is **a.) -1**.