The function `f(x) = "max"{(1-x), (1+x), 2}, x in (-oo, oo)` is

Options

A. Continuous at all points
B. Differentiable at all points
C. Differentiable at all points except at `x=1 and x=-1`
D. Continuous at all points except at `x=1 and x=-1`, where it is discontinuous

Explanation

To solve the question regarding the function \( f(x) = \max\{(1-x), (1+x), 2\} \) for \( x \in (-\infty, \infty) \), we will analyze the three functions involved and determine the overall behavior of \( f(x) \).

### Step-by-Step Solution:

1. **Identify the Functions**:
We have three functions to consider:
- \( g_1(x) = 1 - x \)
- \( g_2(x) = 1 + x \)
...