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

1. stottrupbailey

$y=\sqrt(x^2+7x)$

2. Prebz

x(y) = 1/2 (-7±sqrt(4 y^2+49))

3. stottrupbailey

so far I have it down to $x^2=y^2+7y$

4. stottrupbailey

I'm just kind of confused

5. zepdrix

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

6. stottrupbailey

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

7. zepdrix

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

8. zepdrix

Confused about the completing the square step though?

9. stottrupbailey

yeah a little

10. Prebz

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

11. zepdrix

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

12. zepdrix

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.

13. stottrupbailey

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

14. zepdrix

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