Certainly! Let's evaluate the function [tex]\( F(x) = 2x^3 - x^2 - 4x + 9 \)[/tex] for [tex]\( x = 3 \)[/tex].
1. First, substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( F(x) \)[/tex].
[tex]\[
F(3) = 2(3)^3 - (3)^2 - 4(3) + 9
\][/tex]
2. Next, calculate each term individually:
- [tex]\( (3)^3 = 27 \)[/tex]
- So, [tex]\( 2(3)^3 = 2 \cdot 27 = 54 \)[/tex]
- [tex]\( (3)^2 = 9 \)[/tex]
- Thus, [tex]\( - (3)^2 = - 9 \)[/tex]
- Then, [tex]\( 4(3) = 12 \)[/tex]
3. Now, combine all the terms:
[tex]\[
F(3) = 54 - 9 - 12 + 9
\][/tex]
4. Finally, perform the arithmetic operations:
[tex]\[
54 - 9 = 45
\][/tex]
[tex]\[
45 - 12 = 33
\][/tex]
[tex]\[
33 + 9 = 42
\][/tex]
So, the value of [tex]\( F(3) \)[/tex] is 42. Therefore, the correct answer is:
D. 42
