Which types of mutations in the lac operon stop escherichia coli from utilizing lactose as a carbon source?

The answer is deletion, addition, substitution, and inversion mutations. These types of mutation would result in a nonfunctional protein (beta-galactosidase) that is unable to hydrolyze lactose to galactose and glucose. A deletion or addition upstream of the gene could result in a frameshift mutation that would lead to translation of totally different protein hence the bacteria becomes incapable of using lactose for energy.