3 of 53 of 5 Items

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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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:

\[ \boxed{5} \]