## ajdirig Group Title Can anyone help find the inverse of the fxn: y=x^(2)+4x-6 one year ago one year ago

1. satellite73 Group Title

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

2. ajdirig Group Title

there are 2 inverses, depending on the chosen domain

3. ajdirig Group Title

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

4. satellite73 Group Title

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 $x=-2\pm\sqrt{y+10}$

5. ajdirig Group Title

where did the +4 come from?

6. satellite73 Group Title

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

7. satellite73 Group Title

aka "completing the square"

8. ajdirig Group Title

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

9. satellite73 Group Title

yw

10. ajdirig Group Title

satellite73 do you know the domains?

11. satellite73 Group Title

sure it is given by the plus minus part

12. ajdirig Group Title

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

13. satellite73 Group Title

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

14. ajdirig Group Title

Ok, thank you

15. satellite73 Group Title

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