Final answer:
The mutation in the repressor of an inducible operon that prevents it from binding to the operator would result in the continuous transcription of the operon's genes, as the repressor is unable to inhibit transcription in the absence of an inducer.
Step-by-step explanation:
If the repressor of an inducible operon were mutated so it could not bind the operator, the consequence would be continuous transcription of the operon's genes. This is because the repressor protein is responsible for preventing transcription when the inducer is not present by binding to the operator. If it cannot bind, it is unable to block RNA polymerase from transcribing the genes necessary for metabolizing the inducer, such as lactose in the case of the lac operon.
For the lac operon, which is an inducible system, the presence of lactose inactivates the repressor, allowing the operon's genes to be transcribed. However, if the repressor cannot bind to the operator, even in the absence of lactose, the genes would be continually expressed.
Similarly, for the trp operon, a repressible system, the repressor binds the operator when tryptophan levels are sufficient, inhibiting transcription. If the repressor could not bind, the genes for tryptophan synthesis would be continuously transcribed regardless of tryptophan levels in the cell.