Determine the x-intercepts of the function $$ g(x) = \cos(x) - 1 $$.

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To find the **x-intercepts** of the function $$ g(x) = \cos(x) - 1 $$, we need to determine the values of $$ x $$ for which $$ g(x) = 0 $$.

### Step-by-Step Solution:

1. **Set the function equal to zero:**
   $$
   \cos(x) - 1 = 0
   $$

2. **Solve for $$ \cos(x) $$:**
   $$
   \cos(x) = 1
   $$

3. **Determine the values of $$ x $$ where $$ \cos(x) = 1 $$:**
   
   The cosine function equals 1 at all angles that are integer multiples of $$ 2\pi $$. This is because the cosine function has a period of $$ 2\pi $$, and it reaches its maximum value of 1 at these points.

Therefore:
   $$
   x = 2\pi k \quad \text{where } k \text{ is any integer}
   $$

### Conclusion:

All **x-intercepts** of the function $$ g(x) = \cos(x) - 1 $$ occur at angles that are integer multiples of $$ 2\pi $$.

**Mathematically, the x-intercepts are:**
$$
x = 2\pi k \quad \text{for all integers } k
$$

### Example:

- $$ k = 0 $$: $$ x = 0 $$
- $$ k = 1 $$: $$ x = 2\pi $$
- $$ k = -1 $$: $$ x = -2\pi $$
- $$ k = 2 $$: $$ x = 4\pi $$
- And so on.

These are the points where the graph of $$ g(x) $$ intersects the x-axis.

**Graphical Illustration:**

![Graph of g(x) = cos(x) - 1 showing x-intercepts at multiples of 2π](https://i.imgur.com/YourImageLink.png)

*(Replace the image link with an actual graph if needed.)*

**Final Answer:**
All real numbers equal to an even multiple of π. In other words, every x with x = 2 π k for some integer k.
The x-intercepts of the function $$ g(x) = \cos(x) - 1 $$ are all integer multiples of $$ 2\pi $$.

Determine the x-intercepts of the function \( g(x) = \cos(x) - 1 \).

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