Signal processing question explanation

Question

We have the system :

$$y(k)= |x(k)| +x(-k) + 2x(k-2)$$

In my book it says that this system is not causal and also not stable. I would like a detailed explanation.

Edit : its y(k)

Answer 1

The system is not causal since, for example, at $k = -1$, the value of $y(k)$ depends of the future value of $x$ at $k = 1$.

The system is BIBO stable. Suppose that $|x(k)| \leq B$ for all $k$, then $$ |y(k)| = \left||x(k)| + x(-k) + 2x(k-2)\right|\leq B + B + 2B = 4B $$