College

Thank you for visiting Given the function tex f x 4 x 5 3 tex for what values of tex x tex is tex f x 15 tex A. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Given the function [tex]f(x)=4|x-5|+3[/tex], for what values of [tex]x[/tex] is [tex]f(x)=15[/tex]?

A. [tex]x=2, x=8[/tex]
B. [tex]x=1.5, x=8[/tex]
C. [tex]x=2, x=7.5[/tex]
D. [tex]x=0.5, x=7.5[/tex]

Answer :

To solve the problem:

Given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex], we want to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].

1. Start with the equation:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]

2. Subtract 3 from both sides to simplify the equation:
[tex]\[
4|x - 5| = 12
\][/tex]

3. Divide both sides by 4 to isolate the absolute value:
[tex]\[
|x - 5| = 3
\][/tex]

4. The absolute value equation [tex]\( |x - 5| = 3 \)[/tex] means there are two scenarios to consider:
- Scenario 1: [tex]\( x - 5 = 3 \)[/tex]
- Scenario 2: [tex]\( x - 5 = -3 \)[/tex]

5. Solve for [tex]\( x \)[/tex] in each scenario:
- For Scenario 1:
[tex]\[
x - 5 = 3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 8
\][/tex]

- For Scenario 2:
[tex]\[
x - 5 = -3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 2
\][/tex]

So, the values of [tex]\( x \)[/tex] for which the function [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex]. Therefore, the correct answer is:

[tex]\( x = 2, x = 8 \)[/tex]

Thank you for reading the article Given the function tex f x 4 x 5 3 tex for what values of tex x tex is tex f x 15 tex A. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions