Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = 2x^3 - x^2 + 1 \)[/tex], we need to substitute [tex]\( x = 3 \)[/tex] into the function and evaluate.
Here are the steps:
1. Cube the value of 3:
[tex]\[
3^3 = 27
\][/tex]
2. Multiply the cube by 2:
[tex]\[
2 \times 27 = 54
\][/tex]
3. Square the value of 3:
[tex]\[
3^2 = 9
\][/tex]
4. Subtract the squared result from the previous product:
[tex]\[
54 - 9 = 45
\][/tex]
5. Add 1 to the result:
[tex]\[
45 + 1 = 46
\][/tex]
So, [tex]\( f(3) = 46 \)[/tex].
Therefore, the correct answer is C. 46.
Here are the steps:
1. Cube the value of 3:
[tex]\[
3^3 = 27
\][/tex]
2. Multiply the cube by 2:
[tex]\[
2 \times 27 = 54
\][/tex]
3. Square the value of 3:
[tex]\[
3^2 = 9
\][/tex]
4. Subtract the squared result from the previous product:
[tex]\[
54 - 9 = 45
\][/tex]
5. Add 1 to the result:
[tex]\[
45 + 1 = 46
\][/tex]
So, [tex]\( f(3) = 46 \)[/tex].
Therefore, the correct answer is C. 46.