1. The problem asks to find the function $g(x,y,z)$ given that $g(x,y,2) = |x + 2z + \sqrt{1 - 2y}|$. 2. Notice that the function is given with the third variable fixed as 2, so we want to express $g(x,y,z)$ in a general form. 3. Since the expression includes $2z$ and the value of $z$ is fixed to 2 in the given function, we can infer that the function depends linearly on $z$ as $2z$. 4. Therefore, the general form of the function is: $$g(x,y,z) = |x + 2z + \sqrt{1 - 2y}|$$ 5. This matches the given function when $z=2$, so this is the function $g(x,y,z)$. Final answer: $$g(x,y,z) = |x + 2z + \sqrt{1 - 2y}|$$