Two Solutions of a Double Composition

★ 8/10functions Extrema Substitution Monotonicity

Problem

Let

f(x) = \begin{cases} -\dfrac{1}{2}x, & x > 0,\\ -e^{-x}, & x \leqslant 0. \end{cases}

If the equation $f(f(x)) = m$ has exactly two real solutions $x_1, x_2$ , find the minimum value of $4x_1 + x_2$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, Substitution, Monotonicity

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