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 is $f(3)$ ?

Step 1 ：Substitute \(x=3\) into the function \(f(x)=\frac{1}{2}x+3\): \[f(3)=\frac{1}{2}(3)+3\]

Step 2 ：Simplify the expression: \[f(3)=\frac{3}{2}+3\]

Step 3 ：Convert the mixed number to an improper fraction: \[f(3)=\frac{3}{2}+\frac{6}{2}\]

Step 4 ：Add the fractions: \[f(3)=\frac{9}{2}\]

Step 5 ：Convert the improper fraction to a decimal: \[f(3)=4.5\]

Step 6 ：\(\boxed{f(3)=4.5}\)