Six Zeros of a Composition

★ 8/10functions Extrema Monotonicity Casework

Problem

Let

f(x) = \begin{cases} x(x-t)^2, & x \leqslant t,\\ \dfrac{x}{4}, & x > t, \end{cases} \qquad t > 0.

If the function $g(x) = f\left(f(x) - 1\right)$ has exactly $6$ zeros, find the range of possible values of $t$ .

Answer

Solution

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

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