To solve this problem, we need to follow these steps:
1. Define the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = x^2 + 1
\][/tex]
2. Calculate [tex]\( f(4) \)[/tex]:
Substitute [tex]\( x = 4 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(4) = 4^2 + 1
\][/tex]
Compute the value inside the function:
[tex]\[
4^2 = 16
\][/tex]
Then add 1:
[tex]\[
f(4) = 16 + 1 = 17
\][/tex]
3. Calculate [tex]\( 2 \cdot f(4) \)[/tex]:
Now that we have [tex]\( f(4) = 17 \)[/tex], we need to find twice this value:
[tex]\[
2 \cdot f(4) = 2 \cdot 17
\][/tex]
Finally, compute the product:
[tex]\[
2 \cdot 17 = 34
\][/tex]
So, the value of [tex]\( 2 \cdot f(4) \)[/tex] is [tex]\( \boxed{34} \)[/tex].
