**Core Concept**
In the context of a haemodynamically unstable patient with suspected liver injury due to blunt trauma, the initial investigation aims to quickly assess the severity of the injury and guide immediate management. The patient's unstable condition necessitates a rapid, non-invasive assessment of the liver's integrity and potential haemorrhage.

**Why the Correct Answer is Right**
The first investigation performed in the emergency room is an **Focused Assessment with Sonography for Trauma (FAST)**. This bedside ultrasound examination evaluates for free intraperitoneal fluid, which may indicate internal bleeding. FAST involves scanning four regions: the hepatorenal recess (Morison's pouch), the splenorenal recess, the pelvic region, and the cardiac region. The presence of free fluid in these areas suggests potential liver injury or other intra-abdominal bleeding.

**Why Each Wrong Option is Incorrect**
**Option A:** Non-contrast CT scan of the abdomen is not the first investigation in a haemodynamically unstable patient due to its time-consuming nature and the need for transporting the patient to the radiology department.
**Option B:** Plain abdominal X-ray is not useful in assessing liver injury and may not detect free fluid or other intra-abdominal bleeding.
**Option C:** Abdominal angiography is an invasive procedure that may not be feasible in an unstable patient and is typically reserved for patients with confirmed haemorrhage.

**Clinical Pearl / High-Yield Fact**
In a haemodynamically unstable patient with suspected liver injury, remember the **FAST** mnemonic for the regions to be scanned: **F** (hepatorenal recess), **A** (splenorenal recess), **S** (splenic region), and **T** (pelvic region).

**Correct Answer:** C. Abdominal angiography is not the first step.