What is the domain of #g(x)=x^3=1#?
I assume that there is a typo in the equation and the second equality sign should be either + or - sign.
If the above assumption is correct then (no matter if it is + or -) then the function is a polynomial, so its domain is the whole
Generally to find the domain of a function you need to look for any values which can be excluded from the domain (i.e. the values for which the function's value is undefined).
Such numbers can be found if the function's formula has:
variable in the denominator - then you have to exclude those values of
#x#for which denominator becomes zero
variable under square root sign (or more generally root of an even degree) - this expression can only be calculated if the expression is non negative (zero or positive)
logarithms - these can only be calculated for positive values.