Question 1179038
Here's how to graph f and f⁻¹ and find their domain and range:

**1. Graph f(x) = 3x - 2:**

* This is a linear function with a slope of 3 and a y-intercept of -2.
* Plot the y-intercept (0, -2).
* Use the slope to find another point: from (0, -2), move up 3 units and right 1 unit to get (1, 1).
* Draw a solid line through these points.

**2. Find f⁻¹(x):**

* Replace f(x) with y: y = 3x - 2
* Swap x and y: x = 3y - 2
* Solve for y:
    * x + 2 = 3y
    * y = (x + 2) / 3
* Replace y with f⁻¹(x): f⁻¹(x) = (x + 2) / 3

**3. Graph f⁻¹(x) = (x + 2) / 3:**

* This is also a linear function with a slope of 1/3 and a y-intercept of 2/3.
* Plot the y-intercept (0, 2/3).
* Use the slope to find another point: from (0, 2/3), move up 1 unit and right 3 units to get (3, 5/3).
* Draw a dashed line through these points.

**4. Domain and Range:**

* **f(x) = 3x - 2:**
    * Domain: All real numbers (-∞, ∞)
    * Range: All real numbers (-∞, ∞)
* **f⁻¹(x) = (x + 2) / 3:**
    * Domain: All real numbers (-∞, ∞)
    * Range: All real numbers (-∞, ∞)

**Note:**

* The graphs of f and f⁻¹ are reflections of each other across the line y = x.
* Since both functions are linear, their domains and ranges are all real numbers.