# Thread: Domain Of Functions

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) ?

Thaks in advance for your answers !!!

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) ?

Thaks in advance for your answers !!!
$\displaystyle f(x) = \log_x(4)$

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

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

in my opinion, it's a typo.

3. ## Reply

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...

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

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 $\displaystyle (a,\infty ), (-\infty, \infty ), (-\infty, b]$ 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.

5. ## Reply

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)