Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To find the inverse of the function [tex]\( f(x) = \frac{3x - 5}{7} \)[/tex], let's follow a step-by-step process:
1. Express the function in terms of [tex]\( y \)[/tex]:
[tex]\[ y = \frac{3x - 5}{7} \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to begin solving for the inverse function:
[tex]\[ x = \frac{3y - 5}{7} \][/tex]
3. Isolate [tex]\( y \)[/tex]. First, we multiply both sides of the equation by 7 to get rid of the denominator:
[tex]\[ 7x = 3y - 5 \][/tex]
4. Solve for [tex]\( y \)[/tex] by adding 5 to both sides:
[tex]\[ 7x + 5 = 3y \][/tex]
5. Divide both sides by 3 to isolate [tex]\( y \)[/tex]:
[tex]\[ y = \frac{7x + 5}{3} \][/tex]
Thus, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{7x + 5}{3} \][/tex]
So, the correct answer is:
[tex]\[ f^{-1}(x) = \frac{7x + 5}{3} \][/tex]
1. Express the function in terms of [tex]\( y \)[/tex]:
[tex]\[ y = \frac{3x - 5}{7} \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to begin solving for the inverse function:
[tex]\[ x = \frac{3y - 5}{7} \][/tex]
3. Isolate [tex]\( y \)[/tex]. First, we multiply both sides of the equation by 7 to get rid of the denominator:
[tex]\[ 7x = 3y - 5 \][/tex]
4. Solve for [tex]\( y \)[/tex] by adding 5 to both sides:
[tex]\[ 7x + 5 = 3y \][/tex]
5. Divide both sides by 3 to isolate [tex]\( y \)[/tex]:
[tex]\[ y = \frac{7x + 5}{3} \][/tex]
Thus, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{7x + 5}{3} \][/tex]
So, the correct answer is:
[tex]\[ f^{-1}(x) = \frac{7x + 5}{3} \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.