To determine the value of the function [tex]\( f(x) = 2x^2 + 1 \)[/tex] when [tex]\( x = 3 \)[/tex], follow these steps:
1. Identify the function: The given function is [tex]\( f(x) = 2x^2 + 1 \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function: Replace [tex]\( x \)[/tex] with 3 in the function.
[tex]\[
f(3) = 2(3)^2 + 1
\][/tex]
3. Calculate [tex]\( 3^2 \)[/tex]: Compute the square of 3.
[tex]\[
3^2 = 9
\][/tex]
4. Multiply by 2: Multiply the result by 2.
[tex]\[
2 \times 9 = 18
\][/tex]
5. Add 1: Finally, add 1 to the product.
[tex]\[
18 + 1 = 19
\][/tex]
Thus, the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex] is [tex]\( 19 \)[/tex].
So, the correct answer is [tex]\( 19 \)[/tex].
