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For the function [tex]\( f(x) = \left| x^2 - 4x + 8 \right| \)[/tex], complete parts (a)-(d) below.

(a) Evaluate [tex]\( f(6) \)[/tex]. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. [tex]\( f(6) = \ \square \)[/tex] (Simplify your answer.)
B. [tex]\( f(6) \)[/tex] is undefined.

Answer :

GinnyAnswer
To evaluate the function [tex]\( f(x) = \left| x^2 - 4x + 8 \right| \)[/tex] at [tex]\( x = 6 \)[/tex]:

1. Substitute [tex]\( x = 6 \)[/tex] into the expression inside the absolute value:
[tex]\[ f(6) = \left| 6^2 - 4(6) + 8 \right| \][/tex]

2. Compute the expression inside the absolute value:
[tex]\[ 6^2 = 36 \][/tex]
[tex]\[ 4(6) = 24 \][/tex]
[tex]\[ 36 - 24 + 8 = 20 \][/tex]

3. Since 20 is a positive number, the absolute value of 20 is simply 20:
[tex]\[ \left| 20 \right| = 20 \][/tex]

Therefore, the correct choice is:
A. [tex]\( f(6) = \boxed{20} \)[/tex]

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