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 !!!
Definitely not...
While
And
That is, square brackets indicate inclusion of the end point, while round brackets do not.
This is also incorrect. The notation is very commonly used.- infinities are conventionally always excluded from intervals.
Skeeter is correct, I believe... there seems to be a typo. Also,
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?"Also , do i really need (0,1) wouldn't it be better if i only had D(f) = (1,+oo) ?
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.