To determine the value of [tex]\( f(6) \)[/tex] for the function [tex]\( f(x) = 2x^2 + 5\sqrt{x - 2} \)[/tex], follow these steps:
1. Substitute [tex]\( x = 6 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(6) = 2(6)^2 + 5\sqrt{6 - 2}
\][/tex]
2. Calculate [tex]\( (6)^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
3. Multiply this result by 2:
[tex]\[
2 \cdot 36 = 72
\][/tex]
4. Calculate [tex]\( \sqrt{6 - 2} \)[/tex]:
[tex]\[
6 - 2 = 4
\][/tex]
[tex]\[
\sqrt{4} = 2
\][/tex]
5. Multiply this result by 5:
[tex]\[
5 \cdot 2 = 10
\][/tex]
6. Finally, add the two results from steps 3 and 5:
[tex]\[
72 + 10 = 82
\][/tex]
Therefore, the value of [tex]\( f(6) \)[/tex] is [tex]\( \boxed{82} \)[/tex].
