Let's solve the given problem step by step. We have a function [tex]\( f(x) = 2x^2 - 3x + 2 \)[/tex] and we need to compute several expressions involving this function.
Step 1: Compute [tex]\( f(2) \)[/tex]
First, we substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 2(2)^2 - 3(2) + 2
\][/tex]
Calculate each term step by step:
[tex]\[
2(2)^2 = 2 \cdot 4 = 8
\][/tex]
[tex]\[
-3(2) = -6
\][/tex]
[tex]\[
f(2) = 8 - 6 + 2 = 4
\][/tex]
So, [tex]\( f(2) = 4 \)[/tex].
Step 2: Compute [tex]\( f(4) \)[/tex]
Next, we substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
f(4) = 2(4)^2 - 3(4) + 2
\][/tex]
Calculate each term step by step:
[tex]\[
2(4)^2 = 2 \cdot 16 = 32
\][/tex]
[tex]\[
-3(4) = -12
\][/tex]
[tex]\[
f(4) = 32 - 12 + 2 = 22
\][/tex]
So, [tex]\( f(4) = 22 \)[/tex].
Step 3: Compute [tex]\( f(2) + f(4) \)[/tex]
Now we add the values obtained from steps 1 and 2:
[tex]\[
f(2) + f(4) = 4 + 22 = 26
\][/tex]
So, [tex]\( f(2) + f(4) = 26 \)[/tex].
Step 4: Compute [tex]\( f(2) - f(4) \)[/tex]
Finally, we subtract the value of [tex]\( f(4) \)[/tex] from [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) - f(4) = 4 - 22 = -18
\][/tex]
So, [tex]\( f(2) - f(4) = -18 \)[/tex].
Summary of Results
a. [tex]\( f(2) + f(4) = 26 \)[/tex]
b. [tex]\( f(2) - f(4) = -18 \)[/tex]
