Let $A=\{\text{-1,0,1,2}\}$ and $B=\{\text{-4,-2,0,2}\} and $f,g: A $\rightarrow B$ be functions defined by $f(x)=x^2-x, \;x \in A$ and $g(x)=2 |x- \frac {1} {2} | -1,\; x \in A$. Are $f$ and $g$ equal?

Question

Justify your answer. [Hint: One may note that two functions \(f : A \to B \) and \( g : A \to B \) such that \(f(a) = g(a) \forall \;a \in A,\) are called equal functions.]