**Core Concept**
Hypothyroidism is a condition characterized by reduced production of thyroid hormones, which are essential for various metabolic processes. The best investigation for hypothyroidism should be able to accurately measure the levels of these hormones in the blood.

**Why the Correct Answer is Right**
The most sensitive investigation for hypothyroidism is the measurement of _free thyroxine (FT4)_ levels. FT4 is the biologically active form of thyroxine, and its levels are directly proportional to the body's demand for thyroid hormones. Elevated levels of thyroid-stimulating hormone (TSH) can also indicate hypothyroidism, but measuring FT4 levels provides a more direct assessment of thyroid function. This is because FT4 levels can be influenced by changes in thyroid-binding globulin (TBG) levels, which can occur in conditions such as nephrotic syndrome.

**Why Each Wrong Option is Incorrect**
**Option A:** Total thyroxine (TT4) measurement is less sensitive than FT4 measurement because it is affected by changes in TBG levels.

**Option B:** Triiodothyronine (T3) measurement is not the best option because it is the least sensitive marker of thyroid function.

**Option C:** Thyroid-stimulating hormone (TSH) measurement is useful for screening, but it is not the most sensitive investigation for hypothyroidism because it can be affected by changes in thyroid function at the level of the pituitary gland.

**Clinical Pearl / High-Yield Fact**
When interpreting thyroid function tests, it is essential to consider the patient's clinical context and the results of other investigations, as a normal TSH level does not necessarily rule out hypothyroidism.

**Correct Answer: B. Triiodothyronine (T3) measurement is not the best option because it is the least sensitive marker of thyroid function.