To find [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex] for the function [tex]\( f(x) = 2x^2 + 1 \)[/tex], follow these steps:
1. Substitute the value of [tex]\( x \)[/tex] into the function:
[tex]\[
x = 3
\][/tex]
2. Write down the function:
[tex]\[
f(x) = 2x^2 + 1
\][/tex]
3. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = 2(3^2) + 1
\][/tex]
4. Calculate the square of 3:
[tex]\[
3^2 = 9
\][/tex]
5. Multiply the result by 2:
[tex]\[
2 \cdot 9 = 18
\][/tex]
6. Add 1 to the result:
[tex]\[
18 + 1 = 19
\][/tex]
Therefore, [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex] is [tex]\( 19 \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{19}
\][/tex]
