**Core Concept:** Hirsutism and amenorrhea are clinical manifestations of hormonal imbalances, particularly in females, which can be due to various causes like polycystic ovary syndrome (PCOS), Cushing's syndrome, or drugs.

**Why the Correct Answer is Right:** In this scenario, the correct investigation to determine the underlying cause is a **Dexamethasone suppression test** (DST). This test is used to diagnose Cushing's syndrome, which is a condition characterized by excessive cortisol production, leading to hirsutism and amenorrhea in females.

**Why Each Wrong Option is Incorrect:**

A. **Gonadotropin-releasing hormone (GnRH) stimulation test:** This test is used to diagnose hypothalamic-pituitary disorders, not hormonal overproduction like Cushing's syndrome.

B. **Liver function tests (LFTs):** Although liver dysfunction can affect hormonal balance, LFTs are not specific to diagnose Cushing's syndrome, which mostly affects adrenal function.

C. **Serum cortisol and ACTH levels:** Measuring these hormones can help diagnose Cushing's syndrome, but the DST is more specific and sensitive in detecting cortisol excess and its clinical manifestations.

D. **Imaging studies:** Imaging tests like CT or MRI are used to identify adrenal or pituitary tumors, not diagnose Cushing's syndrome.

**Clinical Pearl:** A positive DST result, showing suppressed cortisol levels after dexamethasone administration, is highly suggestive of Cushing's syndrome, while negative results for other conditions. In this way, the DST helps narrow down the differential diagnosis and guide further management.

**Correct Answer:** C. Serum cortisol and ACTH levels