Final answer:
Iodine is indeed primarily used for the synthesis of thyroid hormones, thyroxine (T4) and triiodothyronine (T3), and insufficient iodine can lead to the development of a goiter.
Step-by-step explanation:
The statement that iodine's only function in the body is the synthesis of thyroid hormones is True. Iodine is critical for the production of thyroxine (T4) and triiodothyronine (T3), which are essential for regulating the body's basal metabolic rate, growth, reproduction, and the activity of the nervous systems. The body transports dietary iodides into the follicular cells of the thyroid, where they are concentrated and used to synthesize T3 and T4. In the absence of sufficient iodine, a goiter can develop due to the accumulation of unusued thyroid precursors.