Answer :

To solve the problem of finding [tex]\( f(-3) + f(4) \)[/tex] for the function [tex]\( f(x) = 3x^3 - 5x + 6 \)[/tex], we will follow these steps:

1. Calculate [tex]\( f(-3) \)[/tex]:
- Substitute [tex]\( -3 \)[/tex] into the function:
[tex]\[
f(-3) = 3(-3)^3 - 5(-3) + 6
\][/tex]
- Calculate the terms inside the function:
- [tex]\( (-3)^3 = -27 \)[/tex]
- [tex]\( 3(-27) = -81 \)[/tex]
- [tex]\( -5(-3) = 15 \)[/tex]
- Sum them up:
[tex]\[
f(-3) = -81 + 15 + 6 = -60
\][/tex]

2. Calculate [tex]\( f(4) \)[/tex]:
- Substitute [tex]\( 4 \)[/tex] into the function:
[tex]\[
f(4) = 3(4)^3 - 5(4) + 6
\][/tex]
- Calculate the terms inside the function:
- [tex]\( 4^3 = 64 \)[/tex]
- [tex]\( 3(64) = 192 \)[/tex]
- [tex]\( -5(4) = -20 \)[/tex]
- Sum them up:
[tex]\[
f(4) = 192 - 20 + 6 = 178
\][/tex]

3. Find [tex]\( f(-3) + f(4) \)[/tex]:
- Add the results from the previous steps:
[tex]\[
f(-3) + f(4) = -60 + 178 = 118
\][/tex]

Therefore, the result of [tex]\( f(-3) + f(4) \)[/tex] is [tex]\( 118 \)[/tex], which corresponds to option b).

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Rewritten by : Barada