To find [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]\[
f(6) = 2(6)^2 + 5\sqrt{6 - 2}
\][/tex]
2. Calculate [tex]\( (6)^2 \)[/tex]:
[tex]\[
(6)^2 = 36
\][/tex]
3. Multiply [tex]\( 2 \)[/tex] by [tex]\( 36 \)[/tex]:
[tex]\[
2 \times 36 = 72
\][/tex]
4. Calculate [tex]\( 6 - 2 \)[/tex]:
[tex]\[
6 - 2 = 4
\][/tex]
5. Find the square root of [tex]\( 4 \)[/tex]:
[tex]\[
\sqrt{4} = 2
\][/tex]
6. Multiply [tex]\( 5 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[
5 \times 2 = 10
\][/tex]
7. Add the two results together:
[tex]\[
72 + 10 = 82
\][/tex]
Therefore, [tex]\( f(6) = 82 \)[/tex].
