Answer :
To solve the problem of finding [tex]\( f(-7) \)[/tex] for the function [tex]\( f(x) = -x^2 + x + 16 \)[/tex], we will substitute [tex]\( x = -7 \)[/tex] into the function and perform the necessary calculations.
Here is the detailed step-by-step solution:
1. Write down the function:
[tex]\[
f(x) = -x^2 + x + 16
\][/tex]
2. Substitute [tex]\( x = -7 \)[/tex] into the function:
[tex]\[
f(-7) = -(-7)^2 + (-7) + 16
\][/tex]
3. Calculate [tex]\((-7)^2\)[/tex]:
[tex]\[
(-7)^2 = 49
\][/tex]
4. Substitute [tex]\(49\)[/tex] back into the equation:
[tex]\[
f(-7) = -49 + (-7) + 16
\][/tex]
5. Simplify the expression step-by-step:
[tex]\[
f(-7) = -49 - 7 + 16
\][/tex]
6. Combine [tex]\(-49\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[
-49 - 7 = -56
\][/tex]
7. Add [tex]\(16\)[/tex] to [tex]\(-56\)[/tex]:
[tex]\[
-56 + 16 = -40
\][/tex]
Therefore, the value of [tex]\( f(-7) \)[/tex] is:
[tex]\[
f(-7) = -40
\][/tex]
Here is the detailed step-by-step solution:
1. Write down the function:
[tex]\[
f(x) = -x^2 + x + 16
\][/tex]
2. Substitute [tex]\( x = -7 \)[/tex] into the function:
[tex]\[
f(-7) = -(-7)^2 + (-7) + 16
\][/tex]
3. Calculate [tex]\((-7)^2\)[/tex]:
[tex]\[
(-7)^2 = 49
\][/tex]
4. Substitute [tex]\(49\)[/tex] back into the equation:
[tex]\[
f(-7) = -49 + (-7) + 16
\][/tex]
5. Simplify the expression step-by-step:
[tex]\[
f(-7) = -49 - 7 + 16
\][/tex]
6. Combine [tex]\(-49\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[
-49 - 7 = -56
\][/tex]
7. Add [tex]\(16\)[/tex] to [tex]\(-56\)[/tex]:
[tex]\[
-56 + 16 = -40
\][/tex]
Therefore, the value of [tex]\( f(-7) \)[/tex] is:
[tex]\[
f(-7) = -40
\][/tex]
