Question

find the domain of the function

g(x) = 2/8-3x

I think answer is {x|x=0} but not sure

Answer 1

"g(x)=2/8-3x" = 4-3x which is probably not the function intended.
Remember when transcribing fractions, it is necessary to add parentheses to the numerator and denominator, and write it as:
g(x)=2/(8-3x)
{x|x=0} means there is only one possible value for x. In fact, the domain is the set of real numbers, except where (8-3x)=0, or x=8/3
You can write it as
(-∞,8/3)∪(8/3,+∞) or
{x|x≠8/3}