An inhibitory transmitter affects the resting membrane potential of the post-synaptic neuron by causing it to:

An inhibitory transmitter functions primarily by increasing the membrane permeability to chloride ions or by opening potassium channels. When these channels are activated, the post-synaptic neuron experiences an influx of negatively charged ions or an efflux of positively charged ions. This process increases the negativity of the inside of the neuron relative to the outside, which leads to hyperpolarization.

Hyperpolarization means that the membrane potential becomes more negative than the resting membrane potential. This change makes it less likely for the neuron to fire an action potential because it creates a larger gap that must be overcome for the neuron to reach its threshold for excitability. Therefore, the role of an inhibitory transmitter in creating hyperpolarization is crucial for regulating neuronal excitability and maintaining balance between excitation and inhibition in the nervous system.

The options that reference myelin sheath development, resistance to muscle relaxants, or simply becoming more negative do not accurately describe the specific actions of inhibitory neurotransmitters on membrane potentials in a post-synaptic neuron.