Answer :
To find the result of [tex]\( f(-3) + f(4) \)[/tex] for the function [tex]\( f(x) = 3x^3 - 5x + 6 \)[/tex], we need to evaluate the function at [tex]\( x = -3 \)[/tex] and [tex]\( x = 4 \)[/tex], and then add those results together.
### Step-by-step Solution:
1. Evaluate [tex]\( f(-3) \)[/tex]:
[tex]\[
f(-3) = 3(-3)^3 - 5(-3) + 6
\][/tex]
- Calculate [tex]\((-3)^3\)[/tex]: [tex]\((-3)^3 = -27\)[/tex]
- Multiply by 3: [tex]\(3 \times (-27) = -81\)[/tex]
- Multiply [tex]\(5 \times (-3)\)[/tex]: [tex]\(5 \times (-3) = -15\)[/tex]
- Add them together: [tex]\(-81 + 15 + 6\)[/tex]
- Simplify: [tex]\(-81 + 15 = -66\)[/tex]
- Finally: [tex]\(-66 + 6 = -60\)[/tex]
So, [tex]\( f(-3) = -60 \)[/tex].
2. Evaluate [tex]\( f(4) \)[/tex]:
[tex]\[
f(4) = 3(4)^3 - 5(4) + 6
\][/tex]
- Calculate [tex]\(4^3\)[/tex]: [tex]\(4^3 = 64\)[/tex]
- Multiply by 3: [tex]\(3 \times 64 = 192\)[/tex]
- Multiply [tex]\(5 \times 4\)[/tex]: [tex]\(5 \times 4 = 20\)[/tex]
- Add them together: [tex]\(192 - 20 + 6\)[/tex]
- Simplify: [tex]\(192 - 20 = 172\)[/tex]
- Finally: [tex]\(172 + 6 = 178\)[/tex]
So, [tex]\( f(4) = 178 \)[/tex].
3. Add the results:
[tex]\[
f(-3) + f(4) = -60 + 178 = 118
\][/tex]
Thus, the result of [tex]\( f(-3) + f(4) \)[/tex] is [tex]\(\boxed{118}\)[/tex]. Therefore, the correct answer is option D) 118.
### Step-by-step Solution:
1. Evaluate [tex]\( f(-3) \)[/tex]:
[tex]\[
f(-3) = 3(-3)^3 - 5(-3) + 6
\][/tex]
- Calculate [tex]\((-3)^3\)[/tex]: [tex]\((-3)^3 = -27\)[/tex]
- Multiply by 3: [tex]\(3 \times (-27) = -81\)[/tex]
- Multiply [tex]\(5 \times (-3)\)[/tex]: [tex]\(5 \times (-3) = -15\)[/tex]
- Add them together: [tex]\(-81 + 15 + 6\)[/tex]
- Simplify: [tex]\(-81 + 15 = -66\)[/tex]
- Finally: [tex]\(-66 + 6 = -60\)[/tex]
So, [tex]\( f(-3) = -60 \)[/tex].
2. Evaluate [tex]\( f(4) \)[/tex]:
[tex]\[
f(4) = 3(4)^3 - 5(4) + 6
\][/tex]
- Calculate [tex]\(4^3\)[/tex]: [tex]\(4^3 = 64\)[/tex]
- Multiply by 3: [tex]\(3 \times 64 = 192\)[/tex]
- Multiply [tex]\(5 \times 4\)[/tex]: [tex]\(5 \times 4 = 20\)[/tex]
- Add them together: [tex]\(192 - 20 + 6\)[/tex]
- Simplify: [tex]\(192 - 20 = 172\)[/tex]
- Finally: [tex]\(172 + 6 = 178\)[/tex]
So, [tex]\( f(4) = 178 \)[/tex].
3. Add the results:
[tex]\[
f(-3) + f(4) = -60 + 178 = 118
\][/tex]
Thus, the result of [tex]\( f(-3) + f(4) \)[/tex] is [tex]\(\boxed{118}\)[/tex]. Therefore, the correct answer is option D) 118.
