Answer :
To solve the problem of finding [tex]\( f(-3) \)[/tex] for the function [tex]\( f(x) = -3x^3 - 4x^2 + 11x + 1 \)[/tex], let's proceed step-by-step:
1. Substitute the value of [tex]\( x \)[/tex]:
We need to evaluate the function at [tex]\( x = -3 \)[/tex]. This means we'll substitute [tex]\(-3\)[/tex] in place of [tex]\( x \)[/tex] in the function.
2. Calculate each term separately:
- For the term [tex]\(-3x^3\)[/tex]:
[tex]\(-3(-3)^3 = -3 \times (-27) = 81\)[/tex]
- For the term [tex]\(-4x^2\)[/tex]:
[tex]\(-4(-3)^2 = -4 \times 9 = -36\)[/tex]
- For the term [tex]\(11x\)[/tex]:
[tex]\(11 \times (-3) = -33\)[/tex]
- The constant term is simply [tex]\(1\)[/tex].
3. Add all the terms together:
Combine the results from each term:
[tex]\[
81 + (-36) + (-33) + 1 = 81 - 36 - 33 + 1 = 13
\][/tex]
4. Conclusion:
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\( 13 \)[/tex].
The correct answer is [tex]\(\boxed{13}\)[/tex], which matches option c) [tex]\( f(-3) = 13 \)[/tex].
1. Substitute the value of [tex]\( x \)[/tex]:
We need to evaluate the function at [tex]\( x = -3 \)[/tex]. This means we'll substitute [tex]\(-3\)[/tex] in place of [tex]\( x \)[/tex] in the function.
2. Calculate each term separately:
- For the term [tex]\(-3x^3\)[/tex]:
[tex]\(-3(-3)^3 = -3 \times (-27) = 81\)[/tex]
- For the term [tex]\(-4x^2\)[/tex]:
[tex]\(-4(-3)^2 = -4 \times 9 = -36\)[/tex]
- For the term [tex]\(11x\)[/tex]:
[tex]\(11 \times (-3) = -33\)[/tex]
- The constant term is simply [tex]\(1\)[/tex].
3. Add all the terms together:
Combine the results from each term:
[tex]\[
81 + (-36) + (-33) + 1 = 81 - 36 - 33 + 1 = 13
\][/tex]
4. Conclusion:
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\( 13 \)[/tex].
The correct answer is [tex]\(\boxed{13}\)[/tex], which matches option c) [tex]\( f(-3) = 13 \)[/tex].
