Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

If [tex]f(x)=\frac{2x-5}{3}[/tex], what is [tex]f^{-1}(x)[/tex]?

A. [tex]\frac{3}{2x-5}[/tex]
B. [tex]\frac{5-2x}{3}[/tex]
C. [tex]\frac{3x+5}{2}[/tex]
D. [tex]\frac{3y+5}{2}[/tex]


Sagot :

To find the inverse of the function [tex]\( f(x) = \frac{2x - 5}{3} \)[/tex], follow these detailed steps:

1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = \frac{2x - 5}{3} \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = \frac{2y - 5}{3} \][/tex]

3. Solve for [tex]\( y \)[/tex]:
a. Multiply both sides by 3 to eliminate the denominator:
[tex]\[ 3x = 2y - 5 \][/tex]

b. Add 5 to both sides to isolate the term with [tex]\( y \)[/tex]:
[tex]\[ 3x + 5 = 2y \][/tex]

c. Divide both sides by 2 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{3x + 5}{2} \][/tex]

4. Therefore, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{3x + 5}{2} \][/tex]

Among the given options, the correct answer is:
[tex]\[ \boxed{\frac{3x + 5}{2}} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.