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ajdirig
 2 years ago
Can anyone help find the inverse of the fxn:
y=x^(2)+4x6
ajdirig
 2 years ago
Can anyone help find the inverse of the fxn: y=x^(2)+4x6

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1it is not a one to one function, so it is unlikely that it has an inverse

ajdirig
 2 years ago
Best ResponseYou've already chosen the best response.0there are 2 inverses, depending on the chosen domain

ajdirig
 2 years ago
Best ResponseYou've already chosen the best response.0I have the answer, I just don't understand how to get there

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1ok 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 \[x=2\pm\sqrt{y+10}\]

ajdirig
 2 years ago
Best ResponseYou've already chosen the best response.0where did the +4 come from?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1because \(x^2+4x\neq (x+2)^2\) 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1aka "completing the square"

ajdirig
 2 years ago
Best ResponseYou've already chosen the best response.0ahh, thank you, I never would have thought to complete the square

ajdirig
 2 years ago
Best ResponseYou've already chosen the best response.0satellite73 do you know the domains?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1sure it is given by the plus minus part

ajdirig
 2 years ago
Best ResponseYou've already chosen the best response.0the question is worded strangely, it asks which domains lead to the two inverses

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1vertex of the parabola \(y=x^2+4x6\) is \((2,10)\) so if \(x<2\) the "function" is decreasing, while if \(x>2\) it is increasing

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1therefore if \(x<2\) the inverse is the one with the negative radical, if \(x>2\) use the one with the positive radical yw
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