Question

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Question
Given that f(x)=x−1
and g(x)=x^2+3x−6
, find (f+g)(2)
.(1 point)
(f+g)(2)=

Answer 1

To find \((f+g)(2)\), we first need to define the functions \(f(x)\) and \(g(x)\) based on the information given:

1. \(f(x) = x - 1\)
2. \(g(x) = x^2 + 3x - 6\)

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:

1. \(2^2 = 4\)
2. \(4(2) = 8\)
3. 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:

\[
\boxed{5}
\]