A Fixed Interval of a Function

Problem

Let

f(x) = -\frac{2x}{1 + |x|}, \qquad x \in \mathbb{R},

and let $M = [a, b]$ with $a < b$ , $N = \{y \mid y = f(x),\ x \in M\}$ . If $M = N$ , find $b - a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Monotonicity, Symmetry

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