Given two functions, \(f(x) = \sqrt{x-2}\) and \(g(x) = \frac{1}{x+3}\) , find the domain of the sum of the functions \(f(x) + g(x)\).

Step 1 ：Step 1: Find the domain of each function separately. The domain of \(f(x) = \sqrt{x-2}\) is \(x \geq 2\) because the expression under the square root must be non-negative. The domain of \(g(x) = \frac{1}{x+3}\) is \(x \neq -3\) because the denominator of the fraction cannot be zero.

Step 2 ：Step 2: Combine the two domains. The domain of the sum of the functions is the intersection of the domains of the individual functions. Therefore, the domain of \(f(x) + g(x)\) is all \(x\) that satisfy both \(x \geq 2\) and \(x \neq -3\).

Step 3 ：Step 3: Determine the intersection of the two domains. Since \(x = -3\) is not in the domain of \(g(x)\), but \(-3 < 2\), the domain of \(f(x) + g(x)\) is \(x \geq 2\).