To find \((f+g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\) together.
Given:
- \(f(x) = 2x + 1\)
- \(g(x) = x^2 - 7\)
We can calculate \((f+g)(x)\) as follows:
\[ (f+g)(x) = f(x) + g(x) = (2x + 1) + (x^2 - 7) \]
Now, we combine the terms:
\[ (f+g)(x) = 2x + 1 + x^2 - 7 \]
\[ (f+g)(x) = x^2 + 2x + (1 - 7) \]
\[ (f+g)(x) = x^2 + 2x - 6 \]
Thus, the result is:
\[ (f+g)(x) = x^2 + 2x - 6 \]