To find \((f+g)(2)\), we first need to define the functions \(f(x)\) and \(g(x)\) based on the information given:
- \(f(x) = x - 1\)
- \(g(x) = x^2 + 3x - 6\)
Now, we can find \((f+g)(x)\) by adding \(f(x)\) and \(g(x)\):
\[ (f+g)(x) = f(x) + g(x) = (x - 1) + (x^2 + 3x - 6) \]
Next, we can simplify this expression:
\[ (f+g)(x) = x - 1 + x^2 + 3x - 6 = x^2 + 4x - 7 \]
Now, we need to find \((f+g)(2)\):
\[ (f+g)(2) = 2^2 + 4(2) - 7 \]
Calculating each term:
- \(2^2 = 4\)
- \(4(2) = 8\)
- Then sum them up: \(4 + 8 - 7\)
Now perform the addition and subtraction:
\[ 4 + 8 = 12 \] \[ 12 - 7 = 5 \]
Therefore, \((f+g)(2) = 5\).
Thus, the final answer is:
\[ \boxed{5} \]