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 973118: 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(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You want the lower branch of the inverse. y%3C-1 is what you want.

4y%5E2%2B4y%2B1=x
4%28y%5E2%2By%2B1%2F4%29=x
4%28y%2B1%2F2%29%5E2=x
%28y%2B1%2F2%29%5E2=x%2F4
y%2B1%2F2=0%2B-+sqrt%28x%29%2F2
y=-1%2F2%2B-+sqrt%28x%29%2F2

Domain x<-1 of the given function corresponds to the lower branch of the inverse function:
highlight%28y=-1%2F2-sqrt%28x%29%2F2%29, this inverse.


Your given function
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C4x%5E2%2B4x%2B1%29
graph is not perfect but includes the whole function.
x less than -1 was specified.

The inverse needed
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C-1%2F2-sqrt%28x%29%2F2%29
graph not perfect. y less than -1 is the range wanted.