Question 1209865
Let's analyze the function f(x) = x + 2⌊x⌋ + √x - 1/|x| to determine its properties.

**1. Natural Domain:**

* **√x:** x ≥ 0
* **1/|x|:** x ≠ 0
* Combining these, the domain is x > 0, or (0, ∞).

**2. Even or Odd:**

* Since the domain is (0, ∞), the function is not symmetric about the y-axis or the origin. Therefore, it cannot be even or odd.

**3. Increasing or Decreasing:**

* **f(x) = x + 2⌊x⌋ + √x - 1/x** (since x > 0, |x| = x)
* Let's analyze the behavior of each term:
    * **x:** Increasing
    * **2⌊x⌋:** Increasing (step function)
    * **√x:** Increasing
    * **-1/x:** Increasing

* Since all terms are increasing over the domain (0, ∞), the function f(x) is **increasing** over its domain.

**4. Invertibility:**

* Since the function is strictly increasing over its domain, it is **invertible**.

**Summary:**

* **Domain:** (0, ∞)
* **Neither even nor odd**
* **Invertible:** Yes
* **Increasing:** Yes
* **Decreasing:** No