Question

suppose $f(x) = -x^2 - 3x + 3$. compute the following:
a.) $f(-5) + f(5) = $
b.) $f(-5) - f(5) = $

Explanation:

Part A: Compute \( f(-5) + f(5) \)

Step 1: Compute \( f(-5) \)

Substitute \( x = -5 \) into \( f(x) = -x^2 - 3x + 3 \):
\[

$$\begin{align*} f(-5) &= -(-5)^2 - 3(-5) + 3 \\ &= -25 + 15 + 3 \\ &= -7 \end{align*}$$

\]

Step 2: Compute \( f(5) \)

Substitute \( x = 5 \) into \( f(x) = -x^2 - 3x + 3 \):
\[

$$\begin{align*} f(5) &= -(5)^2 - 3(5) + 3 \\ &= -25 - 15 + 3 \\ &= -37 \end{align*}$$

\]

Step 3: Compute \( f(-5) + f(5) \)

Add the results from Step 1 and Step 2:
\[
f(-5) + f(5) = -7 + (-37) = -44
\]

Step 1: Use results from Part A

We already know \( f(-5) = -7 \) and \( f(5) = -37 \) from Part A.

Step 2: Compute \( f(-5) - f(5) \)

Subtract \( f(5) \) from \( f(-5) \):
\[
f(-5) - f(5) = -7 - (-37) = -7 + 37 = 30
\]

Answer:

\( -44 \)

Part B: Compute \( f(-5) - f(5) \)