Answer
(f + g)(-1) = 1
Work Step by Step
The notation (f + g)(-1) can be rewritten as f(-1) + g(-1). Solving by adding the functions then evaluating at -1 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 = -1:
h(-1) = $(-1)^{2}$ + (-1) + 1 = 1
Method 2: Evaluate the functions and then add
First we want to evaluate f(x) at x = -1:
f(-1) = -1 + 3 = 2
Then we want to evaluate g(x) at x = -1:
g(-1) = $(-1)^{2}$ - 2 = -1
Add the numbers together:
(f + g)(-1) = 2 + (-1) = 1
Using both methods (f + g)(-1) = 1
