Exercise 5

Let \(A = \{-1, 0, 1, 2\}\), \(B = \{-4, -2, 0, 2\}\) and \(f, g : A \rightarrow B\) be functions defined by
\[ f(x) = x^2 - x,\quad x \in A \]
and
\[ g(x) = 2\left\lfloor x - \frac{1}{2} \right\rfloor,\quad x \in A. \]
Are \(f\) and \(g\) equal?
Justify your answer. (Hint: One may note that two functions \(f : A \rightarrow B\) and \(g : A \rightarrow B\) such that \(f(a) = g(a)\ \forall\ a \in A\), are called equal functions).