**Core Concept:** In pregnancy, medical imaging investigations should prioritize minimizing the risk of radiation exposure to the developing fetus.

**Why the Correct Answer is Right:** The correct answer is **X-rays (radiographs)**, as they are the safest option among the given choices. X-rays use ionizing radiation, which is the least expensive and most widely available form of radiation for imaging. However, unlike other options, X-rays pose significantly lower risk to the fetus compared to other modalities.

**Why Each Wrong Option is Incorrect:**

A. **Ultrasound (Doppler and Echo)**: While ultrasound is the gold standard for imaging during pregnancy, it uses non-ionizing radiation, which is considered safe but not completely risk-free. The misconception lies in the belief that all non-ionizing radiation is entirely safe, which is not entirely accurate.

B. **Mammography:** Mammography involves ionizing radiation and is contraindicated during pregnancy due to the high risk to the fetus.

C. **CT scans:** CT scans use ionizing radiation and pose substantial risk to the developing fetus, making it the least preferred option.

D. **PET scans:** Positron Emission Tomography (PET) scans also involve ionizing radiation, rendering this option unsafe during pregnancy.

**Clinical Pearl:** To ensure safe imaging during pregnancy, it is essential to choose modalities with minimal radiation exposure while considering the clinical necessity of the investigation. Always consult with a radiologist experienced in obstetric imaging to select the safest and most appropriate imaging modality for the patient's condition.

In summary, X-rays are safe for pregnant patients due to their lower radiation dose compared to the alternatives, but it is crucial to weigh the radiation risk against the clinical necessity for each imaging request.