To find the \(y\)-intercepts of the functions \(f(x) = \sqrt{x - 2}\) and \(g(x) = \sqrt{2 - x}\), we substitute \(x = 0\) into both functions and check if they are defined.
For \(f(x) = \sqrt{x - 2}\): \[ f(0) = \sqrt{0 - 2} = \sqrt{-2} \] The function \(f(x)\) is not defined at \(x = 0\) because we cannot take the square root of a negative number. Therefore, \(f(x)\) does not have a \(y\)-intercept.
For \(g(x) = \sqrt{2 - x}\): \[ g(0) = \sqrt{2 - 0} = \sqrt{2} \] The function \(g(x)\) is defined at \(x = 0\), and it has a \(y\)-intercept at the point \((0, \sqrt{2})\).
Since only \(g(x)\) has a \(y\)-intercept, the correct option is:
Option 2: g(x)