Answer
(f/g)(-1) - g(3) = -9
Work Step by Step
The notation (f/g)(-1) - g(3) can be rewritten as f(-1) / g(-1) - g(3). This can be solved by evaluating the two functions at -1 and dividing the two numbers. Lastly, evaluate the function g at 3 and subtract it from the previously found quotient.
In this question:
f(x) = x + 3
g(x) = $x^{2}$ - 2
Evaluate the functions and then divide:
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 - 2 = -1
Divide the numbers:
(f/g)(-1) = 2/ -1 = -2
Evaluate g(3) and subtract:
Evaluate g(x) at x = 3:
g(3) = $3^{2}$ - 2 = 9 - 2 = 7
Add with the previously found product:
(f/g)(-1) - g(3) = -2 - 7 = -9
(f/g)(-1) - g(3) = -9
