Determine the domain of the function f(x) = (2x3 + sin(x)) / ln|x-1|.

Step 1: Solve Question 6.
The function is $f(x) = \frac{2x^3 + \sin(x)}{\ln |x-1|}$.
For the function to be defined, two conditions must be met:

1. The argument of the natural logarithm must be strictly positive: $$|x-1| > 0$$ This implies $x-1 \neq 0$, so $x \neq 1$.
2. The denominator cannot be zero: $$\ln |x-1| \neq 0$$ This implies $|x-1| \neq e^0$, so $|x-1| \neq 1$. This means $x-1 \neq 1$