Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To find the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex], we need to follow these steps:
1. Start by writing the function:
[tex]\[ y = 2x + 1 \][/tex]
2. Swap [tex]\( y \)[/tex] and [tex]\( x \)[/tex] to find the inverse function:
[tex]\[ x = 2y + 1 \][/tex]
3. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
- Subtract 1 from both sides:
[tex]\[ x - 1 = 2y \][/tex]
- Divide both sides by 2:
[tex]\[ y = \frac{x - 1}{2} \][/tex]
4. Rewrite [tex]\( y \)[/tex] as [tex]\( h(x) \)[/tex], which represents the inverse function:
[tex]\[ h(x) = \frac{x - 1}{2} \][/tex]
5. Simplify the expression to match it with the options provided:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
The inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
Thus, the correct answer is:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
1. Start by writing the function:
[tex]\[ y = 2x + 1 \][/tex]
2. Swap [tex]\( y \)[/tex] and [tex]\( x \)[/tex] to find the inverse function:
[tex]\[ x = 2y + 1 \][/tex]
3. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
- Subtract 1 from both sides:
[tex]\[ x - 1 = 2y \][/tex]
- Divide both sides by 2:
[tex]\[ y = \frac{x - 1}{2} \][/tex]
4. Rewrite [tex]\( y \)[/tex] as [tex]\( h(x) \)[/tex], which represents the inverse function:
[tex]\[ h(x) = \frac{x - 1}{2} \][/tex]
5. Simplify the expression to match it with the options provided:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
The inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
Thus, the correct answer is:
[tex]\[ h(x) = \frac{1}{2}x - \frac{1}{2} \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.