Let's find [tex]\( f(2) \)[/tex] for the function [tex]\( f(x) = 2x^2 + 5\sqrt{x+2} \)[/tex].
1. First, substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 2(2)^2 + 5\sqrt{2+2}
\][/tex]
2. Calculate [tex]\( 2(2)^2 \)[/tex]:
[tex]\[
2(2)^2 = 2 \cdot 4 = 8
\][/tex]
3. Next, calculate [tex]\( 5\sqrt{2+2} \)[/tex]:
[tex]\[
5\sqrt{2+2} = 5\sqrt{4} = 5 \cdot 2 = 10
\][/tex]
4. Now, add these two results together:
[tex]\[
f(2) = 8 + 10 = 18
\][/tex]
So, the answer is
[tex]\[
f(2) = 18
\][/tex]
