To find the value of [tex]\( f(2) + f(-1) \)[/tex] for the function [tex]\( f(x) = x^2 - 5x + 1 \)[/tex], we need to follow these steps:
1. Calculate [tex]\( f(2) \)[/tex]:
Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(2) = 2^2 - 5(2) + 1
\][/tex]
Simplify the expression step by step:
[tex]\[
2^2 = 4
\][/tex]
[tex]\[
-5(2) = -10
\][/tex]
Combining these, we get:
[tex]\[
f(2) = 4 - 10 + 1
\][/tex]
[tex]\[
f(2) = -5
\][/tex]
2. Calculate [tex]\( f(-1) \)[/tex]:
Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-1) = (-1)^2 - 5(-1) + 1
\][/tex]
Simplify the expression step by step:
[tex]\[
(-1)^2 = 1
\][/tex]
[tex]\[
-5(-1) = 5
\][/tex]
Combining these, we get:
[tex]\[
f(-1) = 1 + 5 + 1
\][/tex]
[tex]\[
f(-1) = 7
\][/tex]
3. Add the results of [tex]\( f(2) \)[/tex] and [tex]\( f(-1) \)[/tex]:
Now, we need to add [tex]\( f(2) \)[/tex] and [tex]\( f(-1) \)[/tex]:
[tex]\[
f(2) + f(-1) = -5 + 7
\][/tex]
4. Final Result:
[tex]\[
f(2) + f(-1) = 2
\][/tex]
So, the value of [tex]\( f(2) + f(-1) \)[/tex] is [tex]\( \boxed{2} \)[/tex].
