To solve for [tex]\( f(2) \)[/tex] when given the function [tex]\( f(x) = 2x^2 + 5\sqrt{x+2} \)[/tex], follow these steps:
1. Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(2) = 2(2)^2 + 5\sqrt{2 + 2}
\][/tex]
2. Evaluate the squared term [tex]\( (2)^2 \)[/tex]:
[tex]\[
(2)^2 = 4
\][/tex]
3. Multiply the squared term by the coefficient 2:
[tex]\[
2 \times 4 = 8
\][/tex]
4. Substitute [tex]\( x = 2 \)[/tex] into the square root term [tex]\( \sqrt{(2 + 2)} \)[/tex]:
[tex]\[
\sqrt{2 + 2} = \sqrt{4}
\][/tex]
5. Evaluate the square root [tex]\( \sqrt{4} \)[/tex]:
[tex]\[
\sqrt{4} = 2
\][/tex]
6. Multiply the square root term by the coefficient 5:
[tex]\[
5 \times 2 = 10
\][/tex]
7. Add the results of the two terms together:
[tex]\[
8 + 10 = 18
\][/tex]
Therefore, the value of [tex]\( f(2) \)[/tex] is [tex]\( 18 \)[/tex]. [tex]\( f(2) = 18 \)[/tex]
