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

1. amistre64

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

2. anonymous

you mean $x >3$

3. anonymous

?

4. amistre64

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

5. amistre64

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

6. amistre64

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

7. amistre64

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

8. amistre64

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

9. amistre64
10. anonymous

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

11. anonymous

amir.sat is right

12. amistre64

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

13. anonymous

tnx

14. anonymous

amir you defeated the 100level guy

15. amistre64

ive been defeated plenty of times ;)

16. amistre64

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

17. anonymous

lol :)

18. anonymous

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

19. anonymous

amir don't you want to give a question MedaL

20. anonymous

oww yeah

21. anonymous

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