Answer :
To find the value of [tex]\( f(-3) \)[/tex] for the function [tex]\( f(x) = 3x - 4(x + 9)^2 \)[/tex], we should follow these steps:
1. Substitute [tex]\( x = -3 \)[/tex] into the function [tex]\( f(x) \)[/tex].
[tex]\[
f(-3) = 3(-3) - 4((-3) + 9)^2
\][/tex]
2. Simplify the first part of the expression:
[tex]\[
3(-3) = -9
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
(-3) + 9 = 6
\][/tex]
4. Square the result from the previous step:
[tex]\[
6^2 = 36
\][/tex]
5. Multiply the squared result by -4:
[tex]\[
-4 \times 36 = -144
\][/tex]
6. Combine all the simplified parts:
[tex]\[
f(-3) = -9 - 144
\][/tex]
7. Perform the final subtraction:
[tex]\[
-9 - 144 = -153
\][/tex]
So, the value of [tex]\( f(-3) \)[/tex] is [tex]\( -153 \)[/tex].
The correct answer is [tex]\(\boxed{-153}\)[/tex].
1. Substitute [tex]\( x = -3 \)[/tex] into the function [tex]\( f(x) \)[/tex].
[tex]\[
f(-3) = 3(-3) - 4((-3) + 9)^2
\][/tex]
2. Simplify the first part of the expression:
[tex]\[
3(-3) = -9
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
(-3) + 9 = 6
\][/tex]
4. Square the result from the previous step:
[tex]\[
6^2 = 36
\][/tex]
5. Multiply the squared result by -4:
[tex]\[
-4 \times 36 = -144
\][/tex]
6. Combine all the simplified parts:
[tex]\[
f(-3) = -9 - 144
\][/tex]
7. Perform the final subtraction:
[tex]\[
-9 - 144 = -153
\][/tex]
So, the value of [tex]\( f(-3) \)[/tex] is [tex]\( -153 \)[/tex].
The correct answer is [tex]\(\boxed{-153}\)[/tex].
