Post by: TrueTears on December 02, 2008, 05:40:29 pm
This might be a stupid question but when you get something like
And also for this question
Post by: dekoyl on December 02, 2008, 05:41:39 pm
You'll have to do
But
Post by: Mao on December 02, 2008, 05:44:31 pm
- no divide by zero,
- no square root of a negative number,
- no log of a non-positive number,
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
Post by: TrueTears on December 02, 2008, 05:48:30 pm
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?
Post by: TrueTears on December 02, 2008, 06:02:51 pm
Post by: Mao on December 02, 2008, 06:12:21 pm
Post by: TrueTears on December 02, 2008, 06:25:35 pm
Post by: Mao on December 02, 2008, 06:29:15 pm
the set of values you said would be the maximal domain of
Which can be written as
Post by: TrueTears on December 02, 2008, 10:25:29 pm
answer is R
the set of values you said would be the maximal domain of
Which can be written asor
yeap can it also be written as
Also... if you get something like this question :
Post by: Mao on December 02, 2008, 10:51:10 pm
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 >
Post by: dekoyl on December 02, 2008, 11:00:29 pm
Also... if you get something like this question :Mao's probably going to give you a better explanation.(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?
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
Hope you can understand :P
Post by: TrueTears on December 02, 2008, 11:07:31 pm
Post by: Mao on December 03, 2008, 01:59:31 am
Also... if you get something like this question :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)
Post by: TrueTears on December 03, 2008, 01:37:22 pm