To find the value of the function [tex]\( f(x) = 2x^2 + 5\sqrt{x-2} \)[/tex] at [tex]\( x = 6 \)[/tex], we need to substitute [tex]\( x \)[/tex] with 6 in the function and 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 by 2:
[tex]\[
2 \cdot 36 = 72
\][/tex]
4. Calculate the value inside the square root:
[tex]\[
6 - 2 = 4
\][/tex]
5. Take the square root of 4:
[tex]\[
\sqrt{4} = 2
\][/tex]
6. Multiply by 5:
[tex]\[
5 \cdot 2 = 10
\][/tex]
7. Add the results from step 3 and step 6:
[tex]\[
72 + 10 = 82
\][/tex]
Therefore,
[tex]\[
f(6) = 82
\][/tex]
