At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To find the inverse of the function [tex]\( f(x) = \frac{1}{4}x - 12 \)[/tex], follow these steps:
1. Rewrite the function as [tex]\( y = \frac{1}{4}x - 12 \)[/tex]:
[tex]\[ y = \frac{1}{4}x - 12 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[ x = \frac{1}{4}y - 12 \][/tex]
3. Solve the equation for [tex]\( y \)[/tex]:
- First, add 12 to both sides:
[tex]\[ x + 12 = \frac{1}{4}y \][/tex]
- Next, multiply both sides by 4 to isolate [tex]\( y \)[/tex]:
[tex]\[ 4(x + 12) = y \][/tex]
[tex]\[ y = 4x + 48 \][/tex]
4. Therefore, the inverse function [tex]\( h(x) \)[/tex] is:
[tex]\[ h(x) = 4x + 48 \][/tex]
Given the options:
- [tex]\( h(x) = 48x - 4 \)[/tex]
- [tex]\( h(x) = 48x + 4 \)[/tex]
- [tex]\( h(x) = 4x - 48 \)[/tex]
- [tex]\( h(x) = 4x + 48 \)[/tex]
The correct inverse function is:
[tex]\[ h(x) = 4x + 48 \][/tex]
So the correct option is:
[tex]\[ h(x)=4x+48 \][/tex]
1. Rewrite the function as [tex]\( y = \frac{1}{4}x - 12 \)[/tex]:
[tex]\[ y = \frac{1}{4}x - 12 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[ x = \frac{1}{4}y - 12 \][/tex]
3. Solve the equation for [tex]\( y \)[/tex]:
- First, add 12 to both sides:
[tex]\[ x + 12 = \frac{1}{4}y \][/tex]
- Next, multiply both sides by 4 to isolate [tex]\( y \)[/tex]:
[tex]\[ 4(x + 12) = y \][/tex]
[tex]\[ y = 4x + 48 \][/tex]
4. Therefore, the inverse function [tex]\( h(x) \)[/tex] is:
[tex]\[ h(x) = 4x + 48 \][/tex]
Given the options:
- [tex]\( h(x) = 48x - 4 \)[/tex]
- [tex]\( h(x) = 48x + 4 \)[/tex]
- [tex]\( h(x) = 4x - 48 \)[/tex]
- [tex]\( h(x) = 4x + 48 \)[/tex]
The correct inverse function is:
[tex]\[ h(x) = 4x + 48 \][/tex]
So the correct option is:
[tex]\[ h(x)=4x+48 \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.