Answer
(f - g)(0) = 5
Work Step by Step
The notation (f - g)(0) can be rewritten as f(0) - g(0). Solving by subtracting the functions then evaluating at 0 will yield the same result as evaluating each function and then subtracting.
In this question:
f(x) = x + 3
g(x) = $x^{2}$ - 2
Method 1: Subtract the functions then evaluate
First we want to subtract 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 + 5
Evaluate at x = 0:
h(0) = -$(0)^{2}$ + 0 + 5 = 5
Method 2: Evaluate the functions and then subtract
First we want to evaluate f(x) at x = 0:
f(0) = 0 + 3 = 3
Then we want to evaluate g(x) at x = 0:
g(0) = $(0)^{2}$ - 2 = -2
Subtract the numbers together:
(f - g)(0) = 3 - (-2) = 5
Using both methods (f - g)(0) = 5
