Use the functions below.

f(x)=−x−−√3+9

g(x)=−3x−−√3+2

What is (f−g)(x)
?

Enter the missing values.

(1 point)
(f−g)(x)=
$$

1 answer

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:

\[ (f - g)(x) = 2\sqrt{x} + 7 \]