Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Connect with professionals ready to provide precise answers to your questions 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 determine the inverse of the function [tex]\( f(x) = 4x \)[/tex], we can follow these detailed steps:
1. Start with the original function:
[tex]\[ f(x) = 4x \][/tex]
2. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = 4x \][/tex]
3. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ x = \frac{y}{4} \][/tex]
4. Replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] to denote the inverse function [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = \frac{x}{4} \][/tex]
Therefore, the inverse of the function [tex]\( f(x) = 4x \)[/tex] is given by:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
Thus, the correct representation of the inverse function is:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
So, the answer is:
[tex]\[ \boxed{h(x) = \frac{1}{4} x} \][/tex]
1. Start with the original function:
[tex]\[ f(x) = 4x \][/tex]
2. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = 4x \][/tex]
3. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ x = \frac{y}{4} \][/tex]
4. Replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] to denote the inverse function [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = \frac{x}{4} \][/tex]
Therefore, the inverse of the function [tex]\( f(x) = 4x \)[/tex] is given by:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
Thus, the correct representation of the inverse function is:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
So, the answer is:
[tex]\[ \boxed{h(x) = \frac{1}{4} x} \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.