To find [tex]\( f(2) \)[/tex] for the given function [tex]\( f(x) = 2(x)^2 + 5 \sqrt{(x+2)} \)[/tex], follow these steps:
1. 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]\( 2(2)^2 \)[/tex] means [tex]\( 2 \times (2)^2 \)[/tex]
[tex]\( (2)^2 = 4 \)[/tex]
So, [tex]\( 2 \times 4 = 8 \)[/tex]
3. Calculate [tex]\( 5 \sqrt{(2 + 2)} \)[/tex]:
[tex]\( 2 + 2 = 4 \)[/tex]
The square root of 4 is [tex]\( \sqrt{4} = 2 \)[/tex]
So, [tex]\( 5 \times 2 = 10 \)[/tex]
4. Add the results together:
[tex]\( 8 + 10 = 18 \)[/tex]
Thus, [tex]\( f(2) = 18 \)[/tex].
So, the complete statement is:
[tex]\[
f(2) = 18
\][/tex]
