Let . Find…

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let g(t)=∣t−1∣−∣t∣+∣t+1∣, ∀t∈Rg(t) = |t - 1| - |t| + |t + 1|,\ \forall t \in \mathbb{R}. Find f(x)=max⁡{g(t):−32≤t≤x}, ∀x∈(−32,∞)f(x) = \max \{g(t) : -\frac{3}{2} \le t \le x\},\ \forall x \in \left(-\frac{3}{2}, \infty\right).

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