To find the values for the given functions, let’s start by evaluating [tex]\( f(x) \)[/tex] at the given points and then solve the separate parts of the problem.
First, define the function:
[tex]\[ f(x) = -3x^2 + 6x - 9 \][/tex]
### Step 1: Evaluate [tex]\( f(-5) \)[/tex]
We need to substitute [tex]\( x = -5 \)[/tex] into the function:
[tex]\[ f(-5) = -3(-5)^2 + 6(-5) - 9 \][/tex]
[tex]\[ f(-5) = -3(25) + 6(-5) - 9 \][/tex]
[tex]\[ f(-5) = -75 - 30 - 9 \][/tex]
[tex]\[ f(-5) = -114 \][/tex]
### Step 2: Evaluate [tex]\( f(5) \)[/tex]
Now, substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\[ f(5) = -3(5)^2 + 6(5) - 9 \][/tex]
[tex]\[ f(5) = -3(25) + 6(5) - 9 \][/tex]
[tex]\[ f(5) = -75 + 30 - 9 \][/tex]
[tex]\[ f(5) = -54 \][/tex]
### Step 3: Compute [tex]\( f(-5) + f(5) \)[/tex]
Now add the results of [tex]\( f(-5) \)[/tex] and [tex]\( f(5) \)[/tex]:
[tex]\[ f(-5) + f(5) = -114 + (-54) \][/tex]
[tex]\[ f(-5) + f(5) = -168 \][/tex]
### Step 4: Compute [tex]\( f(-5) - f(5) \)[/tex]
Now, subtract the value of [tex]\( f(5) \)[/tex] from [tex]\( f(-5) \)[/tex]:
[tex]\[ f(-5) - f(5) = -114 - (-54) \][/tex]
[tex]\[ f(-5) - f(5) = -114 + 54 \][/tex]
[tex]\[ f(-5) - f(5) = -60 \][/tex]
Therefore, the answers are:
[tex]\[ \text{A. } f(-5) + f(5) = -168 \][/tex]
[tex]\[ \text{B. } f(-5) - f(5) = -60 \][/tex]
