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 of finding the values of [tex]\( x \)[/tex] for which the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex] equals 15, we can follow these steps:

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

2. Isolate the absolute value term:
Start by subtracting 3 from both sides of the equation:
[tex]\[
4|x-5| = 12
\][/tex]

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

4. Break down the absolute value equation:
The equation [tex]\( |x-5| = 3 \)[/tex] consists of two possible cases:
- Case 1: [tex]\( x - 5 = 3 \)[/tex]
- Case 2: [tex]\( x - 5 = -3 \)[/tex]

5. Solve each case:
- For Case 1: [tex]\( x - 5 = 3 \)[/tex]
[tex]\[
x = 3 + 5 = 8
\][/tex]

- For Case 2: [tex]\( x - 5 = -3 \)[/tex]
[tex]\[
x = -3 + 5 = 2
\][/tex]

6. Conclusion:
The values of [tex]\( x \)[/tex] that satisfy the equation [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