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

1. stottrupbailey Group Title

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

2. Prebz Group Title

x(y) = 1/2 (-7±sqrt(4 y^2+49))

3. stottrupbailey Group Title

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

4. stottrupbailey Group Title

I'm just kind of confused

5. zepdrix Group Title

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

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 Group Title

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 Group Title

Confused about the completing the square step though?

9. stottrupbailey Group Title

yeah a little

10. Prebz Group Title

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

11. zepdrix Group Title

$\large x^2+bx$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 Group Title

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 Group Title

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

14. zepdrix Group Title

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