Question

Can anyone help find the inverse of the fxn:
y=x^(2)+4x-6

Answer 1

it is not a one to one function, so it is unlikely that it has an inverse

Answer 2

there are 2 inverses, depending on the chosen domain

Answer 3

I have the answer, I just don't understand how to get there

Answer 4

ok then we can solve via completing the square \[y+6=x^2+4x\]\[y+6+4=(x+2)^2\]
\[y+10=(x+2)^2\] then \[x+2=\pm\sqrt{y+10}\] and so \[x=-2\pm\sqrt{y+10}\]

Answer 5

where did the +4 come from?

Answer 6

because \(x^2+4x\neq (x+2)^2\) however \((x+2)^2=x^2+4x+4\) so when we replace \(x^2+4x\) by \((x+2)^2\) we were adding 4
therefore you have to add 4 to the other side as well

Answer 7

aka "completing the square"

Answer 8

ahh, thank you, I never would have thought to complete the square

Answer 9

yw

Answer 10

satellite73 do you know the domains?

Answer 11

sure it is given by the plus minus part

Answer 12

the question is worded strangely, it asks which domains lead to the two inverses

Answer 13

vertex of the parabola \(y=x^2+4x-6\) is \((-2,-10)\) so if \(x<-2\) the "function" is decreasing, while if \(x>-2\) it is increasing

Answer 14

Ok, thank you

Answer 15

therefore if \(x<-2\) the inverse is the one with the negative radical, if \(x>-2\) use the one with the positive radical
yw