Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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.

Sagot :

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]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.