find f(x) domain
$$f(x)=\log _{x-3}(x ^{2}-1)/(x ^{2}-4)$$

Question

amistre64 · Answer

a few issues that might influence domain are an x under the fraction

the x in the base notation, dont think we can have log_0

and the x on the log argument itself; nothing 0 and under is good

anonymous · Answer

you mean $$x >3 $$

anonymous · Answer

?

amistre64 · Answer

well, lets start with the log argument part:

x^2 - 1 <= 0 is bad

x^2 <= 1

x <= -1 , or x >=1  would be offlimits

amistre64 · Answer

so we are defined by just that to be between -1 and 1

amistre64 · Answer

nothing in the interval makes the bottom look bad so lets try to see if theres anything in there that would make the base part go bad

amistre64 · Answer

there might be some issue in a -base for SOME numbers

amistre64 · Answer

for instance:

log-2(8) = y

8 = (-2)^y  is not defined

amistre64 · Answer

http://xa.yimg.com/kq/groups/4750694/1645343743/name/Negative+Bases+for+Logs.pdf

anonymous · Answer

the domain is this
$$(3,4)\cup(4,+\infty)$$

anonymous · Answer

amir.sat is right

amistre64 · Answer

i messed up on my x^2 - 1 dint i :)

anonymous · Answer

tnx

anonymous · Answer

amir you defeated the 100level guy

amistre64 · Answer

ive been defeated plenty of times ;)

amistre64 · Answer

wolfram would have told me if I was wrong in the end im sure of it lol

anonymous · Answer

lol :)

anonymous · Answer

but i've done that with my self if you have a lot of time i'll show you

anonymous · Answer

amir don't you want to give a question MedaL

anonymous · Answer

oww yeah

anonymous · Answer

$${((-3 + x) (-1 + x^2))/(-4 + x^2)} $$