To solve for [tex]\( f(2 \sqrt{2}) \)[/tex] given the function [tex]\( f(x) = x^2 - 2 \sqrt{2} x + 1 \)[/tex], let's proceed step-by-step:
1. Identify the given function:
[tex]\[
f(x) = x^2 - 2 \sqrt{2} x + 1
\][/tex]
2. Substitute [tex]\( x = 2\sqrt{2} \)[/tex] into the function:
[tex]\[
f(2 \sqrt{2}) = (2 \sqrt{2})^2 - 2 \sqrt{2} (2 \sqrt{2}) + 1
\][/tex]
3. Calculate [tex]\( (2 \sqrt{2})^2 \)[/tex]:
[tex]\[
(2 \sqrt{2})^2 = 4 \times 2 = 8
\][/tex]
4. Calculate [tex]\( 2 \sqrt{2} \times 2 \sqrt{2} \)[/tex]:
[tex]\[
2 \sqrt{2} \times 2 \sqrt{2} = 4 \times 2 = 8
\][/tex]
5. Put the calculated values back into the expression:
[tex]\[
f(2 \sqrt{2}) = 8 - 8 + 1
\][/tex]
6. Simplify the expression:
[tex]\[
8 - 8 + 1 = 1
\][/tex]
Therefore, the value of [tex]\( f(2 \sqrt{2}) \)[/tex] is [tex]\( 1.0 \)[/tex].
