1. ## Domain Of Functions

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) ?

2. Originally Posted by Homo-Sapiens
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) ?

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

$x$ 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.

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.

4. Originally Posted by Bacterius
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.

- 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,

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.

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.

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