Domain Of Functions

Homo-Sapiens · #1 $Old$ November 6th, 2009, 02:17 PM

Hello Everybody ,

I am working on some exercises here , about the domains of some given functions , but my solutions differ than the book ones... Am i wrong in something or the book has indeed mistakes ???

Asks for the domain of the function : f(x) = logx4

The solution it gives me is : D(f) = (0,1)u(1,-oo).

Firstly , why (1,-oo)? i think it's obviously a mistake , what's your opinion?

Also , do i really need (0,1) wouldn't it be better if i only had D(f) = (1,+oo) ?

Thaks in advance for your answers !!!

skeeter · #2 $Old$ November 6th, 2009, 03:35 PM

Quote:

Originally Posted by Homo-Sapiens $View Post$

Hello Everybody ,

I am working on some exercises here , about the domains of some given functions , but my solutions differ than the book ones... Am i wrong in something or the book has indeed mistakes ???

Asks for the domain of the function : f(x) = logx4

The solution it gives me is : D(f) = (0,1)u(1,-oo).

Firstly , why (1,-oo)? i think it's obviously a mistake , what's your opinion?

Also , do i really need (0,1) wouldn't it be better if i only had D(f) = (1,+oo) ?

Thaks in advance for your answers !!!

$f(x) = \log_x(4)$

$x$ is the base of the logarithm ... the base of a log can be any positive value other than 1

$x \in (0,1) \cup (1,\infty)$

in my opinion, it's a typo.

Bacterius · #3 $Old$ November 6th, 2009, 04:48 PM

There are a lot of typo's then, since :
- intervals are written with square brackets for real intervals, and braces for integer intervals, but never round brackets.
- infinities are conventionally always excluded from intervals.

Defunkt · #4 $Old$ November 6th, 2009, 04:53 PM

Quote:

Originally Posted by Bacterius $View Post$

There are a lot of typo's then, since :
- intervals are written with square brackets for real intervals, and braces for integer intervals, but never round brackets.

Definitely not...

$[-1,1] = \{x \in \mathbb{R} : -1 \leq x \leq 1\}$
While
$(-1,1] = \{x \in \mathbb{R} : -1 < x \leq 1\}$
And
$(-1,1) =\{x \in \mathbb{R} : -1 < x < 1\}$

That is, square brackets indicate inclusion of the end point, while round brackets do not.

Quote:

- infinities are conventionally always excluded from intervals.

This is also incorrect. The notation $(a,\infty ), (-\infty, \infty ), (-\infty, b]$ is very commonly used.

Skeeter is correct, I believe... there seems to be a typo. Also,

Quote:

Also , do i really need (0,1) wouldn't it be better if i only had D(f) = (1,+oo) ?

This is not a question of need... It is a question of "can I substitute these values of x to the equation such that it would still hold?"
In this case (for the interval (0,1)), the answer is yes, so it must be included in the answer.

Bacterius · #5 $Old$ November 6th, 2009, 05:13 PM

Then conventions are not exactly "conventions". From where I come (France), we write :

4 < x <= 5 -> x C ]4; 5]

(C is "belongs to", but I have to read this tex tutorial)

And : 3 <= x -> x C [3; +inf[
And : x > 9 -> x C ]-inf; 9[
And for R -> ]-inf; +inf[

Of course, "inf" is the rotated 8, but again the tex tutorial is waiting for me.

I guess the exclude bracket (]-inf) is equivalent to your round bracket ((inf), is that right ? If so then mea culpa, I don't know all math writing in english countries yet since I just moved some weeks ago. I'm only willing to learn but this is going to take some time though.

skeeter · #6 $Old$ November 6th, 2009, 06:19 PM

http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html

Bacterius · #7 $Old$ November 6th, 2009, 06:24 PM

Quote:

Originally Posted by skeeter $View Post$

http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html

In which countries does this notation apply ? (just to know)