Question

The function \( f(x) = \max\left\{(1 - x), (1 + x), 2\right\}, \, x \in (-\infty, \infty) \) is equivalent to

• A. \( f(x) = \left\{ \begin{array}{ll} 1 + x, & x \leq -1 2, & -1 1 - x, & x \geq 1 \end{array} \right. \)
• B. \( f(x) = \left\{ \begin{array}{ll} 2, & -1 1 + x, & x \geq 1 1 - x, & x \leq -1 \end{array} \right. \)
• C. \( f(x) = \left\{ \begin{array}{ll} 1, & -1 1 + x, & x \geq 1 1 - x, & x \leq -1 \end{array} \right. \)
• D. None of the above

Hint:

When working with maximum functions, analyze the behavior of each component function in different intervals to identify the maximum value for each range.

Answer 1

The Correct Option is B