To solve the problem of finding the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 6 \)[/tex] given the function [tex]\( f(x) = 2x^2 + 5 \sqrt{x - 2} \)[/tex], we need to follow these steps:
1. Identify the function and the value of [tex]\( x \)[/tex]:
[tex]\[
f(x) = 2x^2 + 5 \sqrt{x - 2}
\][/tex]
Here, [tex]\( x = 6 \)[/tex].
2. Substitute [tex]\( x = 6 \)[/tex] into the function:
First, replace [tex]\( x \)[/tex] with 6 in the function:
[tex]\[
f(6) = 2(6)^2 + 5 \sqrt{6 - 2}
\][/tex]
3. Calculate the value inside the square root:
[tex]\[
\sqrt{6 - 2} = \sqrt{4} = 2
\][/tex]
4. Square [tex]\( 6 \)[/tex] and multiply by 2:
[tex]\[
2(6)^2 = 2 \times 36 = 72
\][/tex]
5. Multiply the square root result by 5:
[tex]\[
5 \times 2 = 10
\][/tex]
6. Add the two results together to find [tex]\( f(6) \)[/tex]:
[tex]\[
f(6) = 72 + 10 = 82
\][/tex]
Therefore, the value of [tex]\( f(6) \)[/tex] is [tex]\( 82 \)[/tex].
