Determine the domain of the function of two variables.
\[
g(x, y)=\frac{7}{4 y-2 x^{2}}
\]
\[
\{(x, y) \mid y \neq
\]

Step 1 ：The function g(x, y) is defined for all real numbers except for those that make the denominator zero because division by zero is undefined in mathematics.

Step 2 ：The denominator of the function g(x, y) is \(4y - 2x^{2}\). Setting this equal to zero gives us the equation \(4y - 2x^{2} = 0\).

Step 3 ：Solving this equation for y gives us \(y = \frac{x^{2}}{2}\).

Step 4 ：Therefore, the domain of the function g(x, y) is all real numbers (x, y) except for those that satisfy the equation \(y = \frac{x^{2}}{2}\).

Step 5 ：\(\boxed{\text{The domain of the function g(x, y) is } \{(x, y) \mid y \neq \frac{x^{2}}{2}\}}\)