Draw the graph of `f(x) " maximum " {2 sin x, 1 - cos x}, x in (0, pi)`. Also find the range of `g(x) " min " {2 sin x, 1 - cos x}, x in (0, pi)`

Explanation

To solve the problem, we need to draw the graph of the function \( f(x) = \max\{2 \sin x, 1 - \cos x\} \) for \( x \) in the interval \( (0, \pi) \) and find the range of the function \( g(x) = \min\{2 \sin x, 1 - \cos x\} \) for the same interval.

### Step 1: Analyze the Functions
We have two functions to analyze:
1. \( g_1(x) = 2 \sin x \)
2. \( g_2(x) = 1 - \cos x \)

### Step 2: Determine the Values of Each Function
...