Consider the function

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

f(x) = \begin{cases} x - [x] - \frac{1}{2}, & \text{if } x \notin I \\ 0, & \text{if } x \in I \end{cases}

, where

[\cdot]

denotes the greatest integral function and

I

is the set of integers. Find

g(x) = \max\{x^2, f(x), |x|\}

;

-2 \le x \le 2