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 $(f - g)(0) = 5$.
