Let: $g(x)=\frac{1}{x^2-x}$.

1. State the domain of $g$.

   Hint (a):

   Solve for all values for which the denominator is zero. This will make the function undefined. That is, solve $x^2 - x = 0$.

2. Solve for $x$ if $g(x) = 0.5$.

   Step 1 (b):

   Substitute $0.5$ in for $g(x)$.

3. Explain why $g$ does not have an inverse that is a function.

   Hint (c):

   Recall that to create the inverse, reflect the original function over the line $y = x$.