To find the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 2 \)[/tex], follow these steps:
1. Start with the given function:
[tex]\[
f(x) = 2(x^2) + 5\sqrt{x + 2}
\][/tex]
2. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 2(2^2) + 5\sqrt{2 + 2}
\][/tex]
3. Calculate [tex]\( 2^2 \)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
4. Substitute this result back into the equation:
[tex]\[
f(2) = 2(4) + 5\sqrt{4}
\][/tex]
5. Calculate [tex]\( 2(4) \)[/tex]:
[tex]\[
2 \cdot 4 = 8
\][/tex]
6. Simplify the square root of [tex]\( 4 \)[/tex]:
[tex]\[
\sqrt{4} = 2
\][/tex]
7. Substitute the result of the square root into the equation:
[tex]\[
f(2) = 8 + 5(2)
\][/tex]
8. Calculate [tex]\( 5 \cdot 2 \)[/tex]:
[tex]\[
5 \cdot 2 = 10
\][/tex]
9. Add the results:
[tex]\[
8 + 10 = 18
\][/tex]
Thus, the value of the function when [tex]\( x = 2 \)[/tex] is:
[tex]\[
f(2) = 18
\][/tex]
