Math Question

[geoschmo]

Allright, one of you geniuses help me to understand this. http://forum.shrapnelgames.com/images/icons/icon7.gif

I am getting back into school after being out for a few years. Taking a Trig class right now. This question really isn't trig though. More of a review of algebra and geometry before jumping into the trig part of the class. It's probably something I would understand if I had taken algebra more recently. But I don't want to sound stupid and ask the teacher. http://forum.shrapnelgames.com/images/icons/icon7.gif

Question is find the domain and range of
f(x)=sqrt(x+4) (The square root of x+4)

The domain is [-4,infinty)
The correct answer for the range is [0,infinity)

My question is, why isn't the range all real numbers? (-infinity,infinity) In class the teacher worked the problem and he said plug in any domain value for x and see what you get for f(x) is never less then zero.

But isn't there always a positive AND negative number for any square root? If x is 0 for example you get f(0)=sqrt(4) Isn't that 2 or -2? Can someone explain why you don't count the -2?

Geoschmo

[Fyron]

You can not have numbers less than -4 in the domain, as then you would have the square root of a negative number, which is impossible in normal math. This leads to being unable to have a negative number in the range, as there is no way to get a negative number by taking a square root. Any value in the domain leads to a number that is either 0 or positive.

When you have y ^ 2 = x, y can be positive or negative because either a positive or negative value squared can lead to x. But when you have y = x ^ (1/2), you do not have negative numbers, as this is not at all the case of y ^ 2 = x. In the square root case (ignoring complex math, which you are not doing), you are limited to taking square roots of positive numbers (or 0), and square roots are always positive.

[ April 01, 2004, 20:35: Message edited by: Imperator Fyron ]

[Saber Cherry]

In math class, sqrt(x) is defined as "The positive square root of x."

[Yef]

I got a headache of just reading this thread. http://forum.shrapnelgames.com/images/icons/icon10.gif

[Narrew]

Why do I have the picture in my head of Scotty speaking to a modern day computer (they went back in time) "Computer?"..."Computer on"...then he had to do it by hand, just think when we can just ask a computer these tedious questions and can focus on the "ideas" yea right, thats the ticket...

[geoschmo]

Ok, so my problem was simple I guess. I forgot the true mathematical definition of square root. I thought that the sqrt(x²)=x, but that is incorrect. Actually the sqrt(x²)=|x|

[Atrocities]

You guys in five short Posts or so just totally ruined any desire I might have had to return to school. http://forum.shrapnelgames.com/images/icons/icon9.gif

[Baal]

Originally posted by Atrocities:
You guys in five short Posts or so just totally ruined any desire I might have had to return to school. http://forum.shrapnelgames.com/images/icons/icon9.gif <font size="2" face="sans-serif, arial, verdana">Atrocities, you are killing me old boy. Wait for me to get my hands on a camera and I'll show you the most painful math you will ever see.

(I will be back with a picture in a few days; I promise you)

[Dragonswrd]

I might have to take another look at my math books to be able to do trig again, but from what I remember about trig and algebra they were easier when I went back to school to get my degree. http://forum.shrapnelgames.com/images/icons/icon10.gif

[Phoenix-D]

Originally posted by Atrocities:
You guys in five short Posts or so just totally ruined any desire I might have had to return to school. http://forum.shrapnelgames.com/images/icons/icon9.gif <font size="2" face="sans-serif, arial, verdana">Should I post some of my old calc homework and really kill any desire? http://forum.shrapnelgames.com/images/icons/tongue.gif

Or maybe some statatics..

SD = sqrt((sum of y deviations - y average)^2)/n)

[Baal]

Should I post some of my old calc homework and really kill any desire? http://forum.shrapnelgames.com/images/icons/tongue.gif <font size="2" face="sans-serif, arial, verdana">You mean kind like...

[(d^2)z/(dt)^2] + [k/m*z] - [kL/m] + [C/m(dz/dt)] - [g] = [kA/m*sin(wt)]

I have a test involving this problem in about an hour and a half.

[Phoenix-D]

Yep. Fortunately I didn't have to get too deep into calc for my major..even the course I took was a pain.

[Cipher7071]

But isn't there always a positive AND negative number for any square root? If x is 0 for example you get f(0)=sqrt(4) Isn't that 2 or -2? Can someone explain why you don't count the -2?
<font size="2" face="sans-serif, arial, verdana">Geo, this is probably because you are working with functions. A function may only have one value in the range for each value in the domain.
So, in this case, the function sqrt() is defined to be positve .

[geoschmo]

Originally posted by Cipher7071:
</font><blockquote><font size="1" face="sans-serif, arial, verdana">quote:</font><hr /><font size="2" face="sans-serif, arial, verdana"> But isn't there always a positive AND negative number for any square root? If x is 0 for example you get f(0)=sqrt(4) Isn't that 2 or -2? Can someone explain why you don't count the -2?
<font size="2" face="sans-serif, arial, verdana">Geo, this is probably because you are working with functions. A function may only have one value in the range for each value in the domain.
So, in this case, the function sqrt() is defined to be positve . </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Ok, but isn't that circular logic? To me it sounds like you are saying that the square root of a number is always positive, because if it's negative then it's not a function. But the square root being positive is what makes it a function. How do you know it's a function, other then the fact that I typed it in function notation? Because there are times they will give you a problem in function notation and ask you if it is indeed a function.

[Cipher7071]

It is a function by definition. As you continue in math, you find a lot of this. For example, you cannot take a derivative (calculus) of anything that is not a function. It's one those things you have to accept as defined.

[Cipher7071]

In other words:

Take the following two sets of ordered pairs:

f: (1,1), (4,2), (9,3)
g: (1,1), (1,-1), (4,2), (4,-2), (9,3), (9,-3)

f is a function, g is not.

So, if you want to use the square root in circumstances where a function is required,it is useful to define it as f.

[Kimball]

Geo said:

"Question is find the domain and range of
f(x)=sqrt(x+4) (The square root of x+4)

The domain is [-4,infinty)
The correct answer for the range is [0,infinity)

My question is, why isn't the range all real numbers? (-infinity,infinity) In class the teacher worked the problem and he said plug in any domain value for x and see what you get for f(x) is never less then zero."

If you plug in a negative number less that -4, you end up with the square root of a negative number. This is not possible with real numbers, only imaginary, i.e. sqrt(-1) by defintion equals a funny little number called i (or sometimes j).

So:

sqrt(4) = +/- 2 and
sqrt(-4)=2i where 2i=sqrt(4*(-1))=sqrt(4)*sqrt(-1)=2*i

Complex math is, for the most part useless, except when you get into analyzing differential equations and AC electrical circuits. Believe it or not, that imaginary stuff is quite useful in the real world. Well, the real of world of us engineers and other math-type geeks.

[Spoo]

[(d^2)z/(dt)^2] + [k/m*z] - [kL/m] + [C/m(dz/dt)] - [g] = [kA/m*sin(wt)] <font size="2" face="sans-serif, arial, verdana">Hmm... damped, driven, simple harmonic motion?

[narf poit chez BOOM]

Originally posted by Spoo:
</font><blockquote><font size="1" face="sans-serif, arial, verdana">quote:</font><hr /><font size="2" face="sans-serif, arial, verdana"> [(d^2)z/(dt)^2] + [k/m*z] - [kL/m] + [C/m(dz/dt)] - [g] = [kA/m*sin(wt)] <font size="2" face="sans-serif, arial, verdana">Hmm... damped, driven, simple harmonic motion? </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">No. It's obviously a complicated plot to fry my brain.


Say, do you smell smoke? http://forum.shrapnelgames.com/images/icons/shock.gif

[Baal]

Originally posted by Spoo:
</font><blockquote><font size="1" face="sans-serif, arial, verdana">quote:</font><hr /><font size="2" face="sans-serif, arial, verdana"> [(d^2)z/(dt)^2] + [k/m*z] - [kL/m] + [C/m(dz/dt)] - [g] = [kA/m*sin(wt)] <font size="2" face="sans-serif, arial, verdana">Hmm... damped, driven, simple harmonic motion? </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Impressive, it looks like someone else has seen a 3rd year physics course. I managed to shank this very problem on the test I took this morning.

[Cipher7071]

Impressive, it looks like someone else has seen a 3rd year physics course. I managed to shank this very problem on the test I took this morning. <font size="2" face="sans-serif, arial, verdana">I hate it when that happens. http://forum.shrapnelgames.com/images/icons/icon9.gif Must be why I never took 3rd year physics. Too busy frying my brain with Perl scripts.

Hey narf! ... yeah, I think I do smell that smoke. http://forum.shrapnelgames.com/images/icons/icon10.gif

[Slick]

Originally posted by Cipher7071:
</font><blockquote><font size="1" face="sans-serif, arial, verdana">quote:</font><hr /><font size="2" face="sans-serif, arial, verdana">Impressive, it looks like someone else has seen a 3rd year physics course. I managed to shank this very problem on the test I took this morning. <font size="2" face="sans-serif, arial, verdana">I hate it when that happens. http://forum.shrapnelgames.com/images/icons/icon9.gif Must be why I never took 3rd year physics. Too busy frying my brain with Perl scripts.

Hey narf! ... yeah, I think I do smell that smoke. http://forum.shrapnelgames.com/images/icons/icon10.gif </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">I got lucky when I took that stuff. I was taking a physics course which covered SHM, an electrical engineering course which was about RLC circuits and a mechanical engineering course about dynamics of materials. They all revolved around the same formula below hehehe. My homework was almost interchangeable except each class felt that they had to use their own letters. EE's used resistance, inductance and capacitance. ME's used mass, spring constant and damping constant. And the phyisics guys... well they had their hands in everything. Sheez that was about 15 years ago and I still recognize that formula. http://forum.shrapnelgames.com/images/icons/shock.gif

Slick.

[Atrocities]

*Brain Explodes from to much MATH input*

[Kimball]

Originally posted by Slick:
</font><blockquote><font size="1" face="sans-serif, arial, verdana">quote:</font><hr /><font size="2" face="sans-serif, arial, verdana">Originally posted by Cipher7071:
</font><blockquote><font size="1" face="sans-serif, arial, verdana">quote:</font><hr /><font size="2" face="sans-serif, arial, verdana">Impressive, it looks like someone else has seen a 3rd year physics course. I managed to shank this very problem on the test I took this morning. <font size="2" face="sans-serif, arial, verdana">I hate it when that happens. http://forum.shrapnelgames.com/images/icons/icon9.gif Must be why I never took 3rd year physics. Too busy frying my brain with Perl scripts.

Hey narf! ... yeah, I think I do smell that smoke. http://forum.shrapnelgames.com/images/icons/icon10.gif </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">I got lucky when I took that stuff. I was taking a physics course which covered SHM, an electrical engineering course which was about RLC circuits and a mechanical engineering course about dynamics of materials. They all revolved around the same formula below hehehe. My homework was almost interchangeable except each class felt that they had to use their own letters. EE's used resistance, inductance and capacitance. ME's used mass, spring constant and damping constant. And the phyisics guys... well they had their hands in everything. Sheez that was about 15 years ago and I still recognize that formula. http://forum.shrapnelgames.com/images/icons/shock.gif

Slick. </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Funny thing is, second order differential equations like this didn't make sense to me until my mechanical engineering classes started using the spring-mass-damper analogy. That's when the usefulness of Laplace Transforms started showing their true colors. I have even had to apply diff. e.q. to the real world when I had to calculate the CO2 levels in a room at a given time with a given number of people.