Question

what's the inverse function of y= sqrt(x^2 + 7x) please help! :)

Answer 1

\[y=\sqrt(x^2+7x)\]

Answer 2

x(y) = 1/2 (-7±sqrt(4 y^2+49))

Answer 3

so far I have it down to \[x^2=y^2+7y \]

Answer 4

I'm just kind of confused

Answer 5

\[\large y=\sqrt{x^2+7x} \qquad \rightarrow \qquad x=\sqrt{y^2+7y}\]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?

Answer 6

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

Answer 7

Yah there would be a couple more steps to get it there :)
~Taking the square root of both sides,\[\large \pm\sqrt{x^2+\frac{49}{4}}=y+\frac{7}{2}\]

Answer 8

Confused about the `completing the square` step though?

Answer 9

yeah a little

Answer 10

\[y=(\frac{ 1 }{ 2 } (-7±\sqrt{(4 x^2+49)})\]

Answer 11

\[\large x^2+bx\]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,\[\large \left(x+\frac{b}{2}\right)^2\]

Answer 12

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.

Answer 13

the answer prebz gives is the right one, is that what you got zepdrix?

Answer 14

Yah that's the same :) His just has the 1/2 factored out, so it looks nicer.