The domain of the function \[ f(x)=\frac{\sqrt{18+x}}{7-x} \]

Step 1 ：First, consider the expression under the square root, \(18+x\), which must be greater than or equal to 0. This gives us the inequality: \(18 + x \geq 0\).

Step 2 ：Solving for x, we get: \(x \geq -18\).

Step 3 ：Next, consider the denominator, \(7-x\), which cannot be equal to 0. This gives us the equation: \(7 - x \neq 0\).

Step 4 ：Solving for x, we get: \(x \neq 7\).

Step 5 ：Combining these two conditions, the domain of the function is all x such that \(-18 \leq x < 7\) or \(7 < x\).

Step 6 ：In interval notation, this is \([-18, 7) \cup (7, \infty)\).

Step 7 ：So, the domain of the function \(f(x)=\frac{\sqrt{18+x}}{7-x}\) is \(\boxed{[-18, 7) \cup (7, \infty)}\).