Find the domain of the difference of the functions \(f(x) = \sqrt{x}\) and \(g(x) = \frac{1}{x-2}\)

Step 1 ：The domain of a function is the set of all possible input values (typically, the set of x-values) which will produce a valid output from a particular function. We need to consider where both functions are defined.

Step 2 ：The function \(f(x) = \sqrt{x}\) is defined for all \(x \geq 0\). Therefore, the domain of \(f(x)\) is \([0, +\infty)\).

Step 3 ：The function \(g(x) = \frac{1}{x-2}\) is defined for all \(x \neq 2\). Therefore, the domain of \(g(x)\) is \((-\infty, 2) \cup (2, +\infty)\).

Step 4 ：When we find the difference of the functions \(f(x) - g(x)\), the domain will be the intersection of the domains of \(f(x)\) and \(g(x)\).

Step 5 ：The intersection of \([0, +\infty)\) and \((-\infty, 2) \cup (2, +\infty)\) is \([0, 2) \cup (2, +\infty)\).