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#1 2006-11-09 03:50:55

unique
Member
Registered: 2006-10-04
Posts: 419

correct

find the domain of the function defined by the following equation :
f (x) = sqrt(x + 6)

x + 6  > 0
          -

subtract 6 both sides
x < -6
   -

(-00,-6) < is the domain of F

downup ?


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#2 2006-11-09 06:10:19

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: correct

the domain of a function f(x), is the range of x for which the function is valid.

since f(x) = sqrt(x+ 6), you are right in that x + 6 >= 0

so you have that x >= -6. (not <)

and that is youre domain, x >= -6.


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#3 2006-11-09 08:20:49

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: correct

Alternatively, it could be that the domain is only -6, because values of x higher than that give 2 results, meaning the function isn't well-defined.


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It wanted to be normal.

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#4 2006-11-09 11:47:15

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: correct

Correct, mathsy. A function should give a single value for a single input, never a "this OR that" answer.

I guess it depends on what level is being taught. When students are first taught "square root" thay are only taught the positive root, so we should really have a function "psqrt" or something that doesn't suffer from the two-result problem.

So if it is only the positive root then x≥-6 is right, otherwise only -6 is valid.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2006-11-09 14:47:50

polylog
Member
Registered: 2006-09-28
Posts: 162

Re: correct

I thought that whenever the square root sign is written, as in a function definition for example, it means "extract the positive root"... at least it is like that in all the textbooks i've seen. I have never seen any instance where a function definition involving a square root operator was supposed to mean both possible roots.

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#6 2006-11-09 16:58:48

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: correct

The square root of x is a number that, when squared, gives x. So, the square root of 9 is +3 or -3.

I believe that the use of the radical sign √ refers only to the positive root, so you could say:

√9=+3 and -√9=-3

But in most mathematics educations the negative root is not dealt with until much later. But once you learn about it, it tends to stick!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2006-11-09 17:28:57

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: correct

The square root of x is a number that, when squared, gives x. So, the square root of 9 is +3 or -3.

I believe what is typically called the "square root sign" is actually the principal square root sign.

But in most mathematics educations the negative root is not dealt with until much later. But once you learn about it, it tends to stick!

It's not so much us not dealing with something more complex than it is us wanting everything to be a function.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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