The functions $f$ and $g$ are such that \[ \begin{array}{l} f(x)=\frac{1}{2} x+3 \\ g(x)=\frac{14}{2 x-3} \end{array} \] What number cannot be included in the domain of $g$ ?

Step 1 ：Given the functions \(f(x) = \frac{1}{2}x + 3\) and \(g(x) = \frac{14}{2x - 3}\)

Step 2 ：To find the number that cannot be included in the domain of \(g(x)\), we need to find the value of x that makes the denominator of the fraction equal to zero.

Step 3 ：Set the denominator equal to zero: \(2x - 3 = 0\)

Step 4 ：Solve for x: \(x = \frac{3}{2}\)

Step 5 ：\(\boxed{\frac{3}{2}}\) cannot be included in the domain of \(g(x)\)