Let's consider the function [tex]\( f(x) = \frac{2x^2 - 3x + 1}{x + 2} \)[/tex].
To find the values of [tex]\( f(3) + f(1) \)[/tex], follow these steps:
1. Evaluate [tex]\( f(3) \)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = \frac{2(3)^2 - 3(3) + 1}{3 + 2}
\][/tex]
- Calculate the numerator and the denominator separately:
[tex]\[
\text{Numerator} = 2(3)^2 - 3(3) + 1 = 2(9) - 9 + 1 = 18 - 9 + 1 = 10
\][/tex]
[tex]\[
\text{Denominator} = 3 + 2 = 5
\][/tex]
- Therefore,
[tex]\[
f(3) = \frac{10}{5} = 2.0
\][/tex]
2. Evaluate [tex]\( f(1) \)[/tex]:
- Substitute [tex]\( x = 1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(1) = \frac{2(1)^2 - 3(1) + 1}{1 + 2}
\][/tex]
- Calculate the numerator and the denominator separately:
[tex]\[
\text{Numerator} = 2(1)^2 - 3(1) + 1 = 2 - 3 + 1 = 0
\][/tex]
[tex]\[
\text{Denominator} = 1 + 2 = 3
\][/tex]
- Therefore,
[tex]\[
f(1) = \frac{0}{3} = 0.0
\][/tex]
3. Calculate [tex]\( f(3) + f(1) \)[/tex]:
[tex]\[
f(3) + f(1) = 2.0 + 0.0
\][/tex]
[tex]\[
f(3) + f(1) = 2.0
\][/tex]
Therefore, the value of [tex]\( f(3) + f(1) \)[/tex] is [tex]\( \boxed{2.0} \)[/tex].
