Question - Finding Inverse Function by Switching Variables
Solution:
The question asks for the inverse of the function f(x) = (2x+3)/(x+2), evaluated at x = -5. To find the inverse function, f^(-1)(x), you need to switch the roles of x and y in the equation and then solve for y. Here's how:1. Replace f(x) with y:y = (2x + 3)/(x + 2)2. Switch x and y:x = (2y + 3)/(y + 2)3. Solve for y:x(y + 2) = 2y + 3xy + 2x = 2y + 3xy - 2y = 3 - 2xy(x - 2) = 3 - 2xy = (3 - 2x) / (x - 2)Now that we have the inverse function, we can plug in x = -5 to find the value of f^(-1)(-5):f^(-1)(-5) = (3 - 2(-5)) / ((-5) - 2)f^(-1)(-5) = (3 + 10) / (-5 - 2)f^(-1)(-5) = 13 / (-7)f^(-1)(-5) = -13/7So, the value of the inverse function f^(-1) at x = -5 is -13/7.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com