Answer
(f + g)(2) = 7
Work Step by Step
The notation (f + g)(2) can be rewritten as f(2) + g(2). Solving by adding the functions then evaluating at 2 will yield the same result as evaluating each function and then adding together.
In this question:
f(x) = x + 3
g(x) = $x^{2}$ - 2
Method 1: Add the functions then evaluate
First we want to add the two functions. The new function will be called h(x).
h(x) = f(x) + g(x)
h(x) = (x + 3) + ($x^{2}$ - 2)
h(x) = x + 3 + $x^{2}$ - 2
Combine like variables to get:
h(x) = $x^{2}$ + x + 1
Evaluate at x = 2:
h(2) = $2^{2}$ + 2 + 1 = 7
Method 2: Evaluate the functions and then add
First we want to evaluate f(x) at x = 2:
f(2) = 2 + 3 = 5
Then we want to evaluate g(x) at x = 2:
g(2) = $2^{2}$ - 2 = 2
Add the numbers together:
(f + g)(2) = 5 + 2 = 7
Using both methods (f + g)(2) = 7
