Simplify the function f(x,y).

Step 1: Simplify the function $f(x,y)$.
The given function is $f(x,y) = \sqrt{56x^2 - 8y^2 - 16x - 31 + 1 - 8x}$.
First, simplify the expression under the square root:
Let $g(x,y) = 56x^2 - 8y^2 - 16x - 31 + 1 - 8x$.
Combine like terms:

$$g(x,y) = 56x^2 - 8y^2 - (16x + 8x) - (31 - 1)$$ $$$$