At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To find the inverse of the function [tex]\( f(x) = \frac{1}{4}x - 12 \)[/tex], let's go through the following steps:
1. Rewrite the function in terms of y:
[tex]\[ y = \frac{1}{4}x - 12 \][/tex]
2. Swap x and y to find the inverse function:
[tex]\[ x = \frac{1}{4}y - 12 \][/tex]
3. Solve for y in terms of x:
To solve for [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation.
- First, add 12 to both sides:
[tex]\[ x + 12 = \frac{1}{4}y \][/tex]
- Then, multiply both sides by 4 to solve for y:
[tex]\[ 4(x + 12) = y \][/tex]
Simplifying this, we get:
[tex]\[ y = 4x + 48 \][/tex]
Therefore, the inverse function is:
[tex]\[ h(x) = 4x + 48 \][/tex]
Among the provided options, the correct answer is:
[tex]\[ h(x) = 4x + 48 \][/tex]
1. Rewrite the function in terms of y:
[tex]\[ y = \frac{1}{4}x - 12 \][/tex]
2. Swap x and y to find the inverse function:
[tex]\[ x = \frac{1}{4}y - 12 \][/tex]
3. Solve for y in terms of x:
To solve for [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation.
- First, add 12 to both sides:
[tex]\[ x + 12 = \frac{1}{4}y \][/tex]
- Then, multiply both sides by 4 to solve for y:
[tex]\[ 4(x + 12) = y \][/tex]
Simplifying this, we get:
[tex]\[ y = 4x + 48 \][/tex]
Therefore, the inverse function is:
[tex]\[ h(x) = 4x + 48 \][/tex]
Among the provided options, the correct answer is:
[tex]\[ h(x) = 4x + 48 \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.