Help Please

This is the complicated answer given by Wolfram/Alpha:

{x element R : 6 x + sqrt(37)<1 or (6 x + sqrt(13)>1 and 6 x<1 + sqrt(13)) or 6 x>1 + sqrt(37) or 1/6 (1 - sqrt(37))<x<-2/3 or -2/3<x<1/6 (1 - sqrt(13)) or 1/6 (1 + sqrt(13))<x<1 or 1<x<1/6 (1 + sqrt(37))}
(assuming a function from reals to reals). See the link here:

http://www.wolframalpha.com/input/?i=Domain++y%3D+1+%2F+Log(abs%5B3x%5E2+-+x+-+2%5D)&rawformassumption=%7B%22C%22,+%22Domain%22%7D+-%3E+%7B%22DomainAndRangeWord%22%7D&rawformassumption=%7B%22FunClash%22,+%22Log%22%7D+-%3E+%7B%22Log10%22%7D

The absolute value bars mean that this is only undefined when :

3x^2 - x - 2  = 0     factor

(3x + 2) (x - 1)  = 0     set each factor to 0   and x = -2/3    or x =  1

Thus....all x values are in   the domain except  x = -2/3   and x = 1

Here's the graph :  https://www.desmos.com/calculator/uuzamhwcht

CPhill

I tried plugging that in but it wouldn't work

It's also undefined when 3x^2 - x - 2 =1 or -1, since then the log will be zero, and we are not allowed to divide by zero.