Implied(maximal) domain

[TrueTears]

I just want to clear up how to work out maximal domains. For example, if you get something like, "work out the implied domain of
." What i do is, i ask myself "f(x) is defined when....." In this case it is f(x) is defined when So then u solve that equation and u get .

This might be a stupid question but when you get something like do you do ask yourself f(x) is defined when ? Or do you just look at the equation under the square root sign and find the implied domain of that, and that would be the implied domain of ?

And also for this question . Do you just keep in mind the denominator can not equal 0 and work out the implied domain from there? ie, so the numerator has nothing to do with the working out here?  Hence the implied domain will be R\{-1}?

[dekoyl]

Yes. If you get

You'll have to do as anything inside the square root has to be

But is never less than 0 so it's okay to find the implied domain of under the square root in this case.

[Mao]

when finding maximal domains, you have to keep in mind of a few mathematical laws:

 - no divide by zero,

 - no square root of a negative number,

 - no log of a non-positive number, (note that 'a' *can* be a negative number, but then the 'log' would no longer be a continuous function over a range, it'll just be dots)

in the first case, the only relevant law is the square root of neg number, hence you have to ensure that the expression inside the root is not negative.

in the second case, the only relevant law is division by zero, hence you have to ensure that the denominator is not zero

[TrueTears]

Ah, i see dekoyl. So just for clarification, whenever something under the square root can never be larger or equal to 0. You would just look for the implied domain of what is under the square root sign and you will have the implied domain of the f(x)?

Also the "laws" Mao pointed out for implied domain questions, are there any more, like things to look out for when dealing with these questions?

[TrueTears]

totally understand now thanks both mao and dekoyl

[Mao]

answered on MSN

[TrueTears]

opps dw wrong question LOL accident hahaha looked at the answer for the wrong answer >< silly me

[Mao]

answer is R

the set of values you said would be the maximal domain of

Which can be written as or

[TrueTears]

answer is R

the set of values you said would be the maximal domain of

Which can be written as or

yeap can it also be written as ? oh yes sorry should not be greater and equal to etc. Not very used with Latex yet lol forgot to change

Also... if you get something like this question : (the square root is over the whole fraction, not sure how to do it on latex lol) a combination of no divide by 0 and no square root of negative numbers. How would you find the implied domain for this?

[Mao]

, though I dare say my formats are more 'prefered'

note that when we exclude, the boundaries need to be considered. In this case, the boundaries are included, hence we cannot exclude it, i.e. round brackets or < or >

[dekoyl]

Also... if you get something like this question : (the square root is over the whole fraction, not sure how to do it on latex lol) a combination of no divide by 0 and no square root of negative numbers. How would you find the implied domain for this?

Mao's probably going to give you a better explanation.
But there's a lot of "logic" involved.

First, x ≠ -2.
But algebraically, you might get x > -2. However, if x < -2, the whole thing will become a negative on negative, making it positive. Therefore x < -2 (as you will end up with a positive inside a square root). So for example, if x = -3, it'll become
And of course there's the which you can solve.

Hope you can understand

[TrueTears]

ah yes, i see thanks mao and dekoyl once again

[Mao]

Also... if you get something like this question : (the square root is over the whole fraction, not sure how to do it on latex lol) a combination of no divide by 0 and no square root of negative numbers. How would you find the implied domain for this?

Mao's probably going to give you a better explanation.

I shall attempt to

firstly, you might want to take a look at my LaTeX guide, http://vcenotes.com/forum/index.php/topic,3137.0.html
you will find that LaTeX uses '{' and '}' as parenthesis, as opposed to '(' and ')'
so that radical would be

Code: (LaTeX) [Select]

\sqrt{ \frac{x-1}{x+2} }

now, as for the actual radical,

firstly, we note that the expression inside the square root must be non-negative:









hence, the acceptable x values here are

(note that -2 is not included, because division by zero would be naughty)

[TrueTears]

ah yes thank you very much ^.^