SOLUTION: find the inverse of the following function: 4x^2+4x+1, x<-1. Verify answer by composing the inverse with the original function. I switched x and y and got this: (-1+ or - sqrtx) /

Algebra ->  Functions -> SOLUTION: find the inverse of the following function: 4x^2+4x+1, x<-1. Verify answer by composing the inverse with the original function. I switched x and y and got this: (-1+ or - sqrtx) /      Log On


   

Question 973117: find the inverse of the following function: 4x^2+4x+1, x<-1. Verify answer by composing the inverse with the original function.
I switched x and y and got this: (-1+ or - sqrtx) / 2 . I don't know whether it is + or - ? When I plug it back into the original with the negative it doesn't work out. When I plug it in with the positive it works, but it doesn't agree with the domain. thanks for your help
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The description first wants to focus on the domain x%3C-1 for f%28x%29=4x%5E2%2B4x%2B1;
The inverse will use the RANGE of f for its domain, and will use the DOMAIN of f for its range; in other words, the inverse function will switch the domain and range.

The range for f%5E-1%28x%29 will be y%3C-1. The part of the inverse you want will be most of the lower branch and you can judge this better from examining the graphs.

Lower branch of the inverse, means you use the MINUS form.


Other q# already more thoroughly answered.