To find \((f - g)(x)\), we need to subtract the function \(g(x)\) from the function \(f(x)\). Given:
\[ f(x) = -\sqrt{x} + 9 \] \[ g(x) = -3\sqrt{x} + 2 \]
Now, we can perform the subtraction:
\[ (f - g)(x) = f(x) - g(x) \]
Substituting the expressions for \(f(x)\) and \(g(x)\):
\[ (f - g)(x) = (-\sqrt{x} + 9) - (-3\sqrt{x} + 2) \]
Distributing the negative sign:
\[ (f - g)(x) = -\sqrt{x} + 9 + 3\sqrt{x} - 2 \]
Now, combine the like terms:
\[ (f - g)(x) = (-\sqrt{x} + 3\sqrt{x}) + (9 - 2) \]
This simplifies to:
\[ (f - g)(x) = 2\sqrt{x} + 7 \]
Thus, the answer is:
\[ (f - g)(x) = 2\sqrt{x} + 7 \]