To find \((f - g)(x)\), you need to subtract the function \(g(x)\) from \(f(x)\).
Given:
- \(f(x) = 2x + 1\)
- \(g(x) = x^2 - 7\)
The expression for \((f - g)(x)\) can be written as:
\[ (f - g)(x) = f(x) - g(x) \]
Substituting the functions into the equation:
\[ (f - g)(x) = (2x + 1) - (x^2 - 7) \]
Now simplify the expression:
\[ (f - g)(x) = 2x + 1 - x^2 + 7 \]
Combine like terms:
\[ (f - g)(x) = -x^2 + 2x + 8 \]
So, the final result is:
\[ (f - g)(x) = -x^2 + 2x + 8 \]