Answer :
To solve this problem, we need to evaluate the function [tex]\( f(n) = n^2 - 2n \)[/tex] for each given value of [tex]\( n \)[/tex] and compare the results to the options provided. Let's go through each option one by one:
1. Evaluating [tex]\( f(-2) \)[/tex]:
[tex]\[
f(-2) = (-2)^2 - 2(-2) = 4 + 4 = 8
\][/tex]
The option says [tex]\( f(-2) = 0 \)[/tex], but our calculation shows [tex]\( f(-2) = 8 \)[/tex]. Therefore, this option is not correct.
2. Evaluating [tex]\( f(-4) \)[/tex]:
[tex]\[
f(-4) = (-4)^2 - 2(-4) = 16 + 8 = 24
\][/tex]
The option says [tex]\( f(-4) = 24 \)[/tex], which matches our calculation. Therefore, this option is correct.
3. Evaluating [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 1^2 - 2 \times 1 = 1 - 2 = -1
\][/tex]
The option says [tex]\( f(1) = 3 \)[/tex], but our calculation shows [tex]\( f(1) = -1 \)[/tex]. Therefore, this option is not correct.
4. Evaluating [tex]\( f(5) \)[/tex]:
[tex]\[
f(5) = 5^2 - 2 \times 5 = 25 - 10 = 15
\][/tex]
The option says [tex]\( f(5) = 35 \)[/tex], but our calculation shows [tex]\( f(5) = 15 \)[/tex]. Therefore, this option is not correct.
5. Evaluating [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = 2^2 - 2 \times 2 = 4 - 4 = 0
\][/tex]
The option says [tex]\( f(2) = 0 \)[/tex], which matches our calculation. Therefore, this option is correct.
In summary, the correct options based on the evaluations are:
- [tex]\( f(-4) = 24 \)[/tex]
- [tex]\( f(2) = 0 \)[/tex]
1. Evaluating [tex]\( f(-2) \)[/tex]:
[tex]\[
f(-2) = (-2)^2 - 2(-2) = 4 + 4 = 8
\][/tex]
The option says [tex]\( f(-2) = 0 \)[/tex], but our calculation shows [tex]\( f(-2) = 8 \)[/tex]. Therefore, this option is not correct.
2. Evaluating [tex]\( f(-4) \)[/tex]:
[tex]\[
f(-4) = (-4)^2 - 2(-4) = 16 + 8 = 24
\][/tex]
The option says [tex]\( f(-4) = 24 \)[/tex], which matches our calculation. Therefore, this option is correct.
3. Evaluating [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 1^2 - 2 \times 1 = 1 - 2 = -1
\][/tex]
The option says [tex]\( f(1) = 3 \)[/tex], but our calculation shows [tex]\( f(1) = -1 \)[/tex]. Therefore, this option is not correct.
4. Evaluating [tex]\( f(5) \)[/tex]:
[tex]\[
f(5) = 5^2 - 2 \times 5 = 25 - 10 = 15
\][/tex]
The option says [tex]\( f(5) = 35 \)[/tex], but our calculation shows [tex]\( f(5) = 15 \)[/tex]. Therefore, this option is not correct.
5. Evaluating [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = 2^2 - 2 \times 2 = 4 - 4 = 0
\][/tex]
The option says [tex]\( f(2) = 0 \)[/tex], which matches our calculation. Therefore, this option is correct.
In summary, the correct options based on the evaluations are:
- [tex]\( f(-4) = 24 \)[/tex]
- [tex]\( f(2) = 0 \)[/tex]
