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stottrupbailey
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what's the inverse function of y= sqrt(x^2 + 7x) please help! :)
 one year ago
 one year ago
stottrupbailey Group Title
what's the inverse function of y= sqrt(x^2 + 7x) please help! :)
 one year ago
 one year ago

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stottrupbailey Group TitleBest ResponseYou've already chosen the best response.0
\[y=\sqrt(x^2+7x)\]
 one year ago

Prebz Group TitleBest ResponseYou've already chosen the best response.0
x(y) = 1/2 (7±sqrt(4 y^2+49))
 one year ago

stottrupbailey Group TitleBest ResponseYou've already chosen the best response.0
so far I have it down to \[x^2=y^2+7y \]
 one year ago

stottrupbailey Group TitleBest ResponseYou've already chosen the best response.0
I'm just kind of confused
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large y=\sqrt{x^2+7x} \qquad \rightarrow \qquad x=\sqrt{y^2+7y}\]Squaring both sides,\[\large x^2=y^2+7y\]Let's complete the square on y, half of 7, squared, is \(\dfrac{49}{4}\).\[\large x^2+\frac{49}{4}=y^2+7y+\frac{49}{4}\] \[\large x^2+\frac{49}{4}=\left(y+\frac{7}{2}\right)^2\] I think maybe do something like this to deal with the different degrees of y. Does that make sense?
 one year ago

stottrupbailey Group TitleBest ResponseYou've already chosen the best response.0
umm kind of... I'm a little lost at the part where you do the 49/4. This is a homework question online and they want a y= something, equation
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Yah there would be a couple more steps to get it there :) ~Taking the square root of both sides,\[\large \pm\sqrt{x^2+\frac{49}{4}}=y+\frac{7}{2}\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Confused about the `completing the square` step though?
 one year ago

stottrupbailey Group TitleBest ResponseYou've already chosen the best response.0
yeah a little
 one year ago

Prebz Group TitleBest ResponseYou've already chosen the best response.0
\[y=(\frac{ 1 }{ 2 } (7±\sqrt{(4 x^2+49)})\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large x^2+bx\]To complete the square, we take half of the b term, and square it. That is the term we will want to ADD to complete the square.\[\large \left(\frac{b}{2}\right)^2 \qquad \rightarrow \qquad \frac{b^2}{4}\]So to complete the square we would add this term,\[\large x^2+bx+\frac{b^2}{4}\]And since it's a perfect square, we can write it as,\[\large \left(x+\frac{b}{2}\right)^2\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Hmm completing hte square can be a little tricky if you don't remmeber how to do it :( I can't think of the best way to explain it.
 one year ago

stottrupbailey Group TitleBest ResponseYou've already chosen the best response.0
the answer prebz gives is the right one, is that what you got zepdrix?
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Yah that's the same :) His just has the 1/2 factored out, so it looks nicer.
 one year ago
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