Final answer:
To find ((f)/(g))(-1), substitute x = -1 into the functions f(x) and g(x). The value of ((f)/(g))(-1) is -1/7. To find the values not in the domain of (f)/(g), solve g(x) = 0 for x and find that x = 4/3 is not in the domain.
Step-by-step explanation:
(a) Find ((f)/(g))(-1)
To find ((f)/(g))(-1), we need to substitute x = -1 into the functions f(x) and g(x).
f(-1) = -5 + 4(-1)^2 = -5 + 4(1) = -5 + 4 = -1
g(-1) = 4 - 3(-1) = 4 + 3 = 7
((f)/(g))(-1) = (-1)/(7) = -1/7
(b) Find all values that are NOT in the domain of (f)/(a)
To find the values that are not in the domain of (f)/(g), we need to look for values of x that make the denominator g(x) equal to zero.
Setting g(x) = 0 and solving for x:
4 - 3x = 0
-3x = -4
x = -4/(-3) = 4/3
Therefore, the value x = 4/3 is not in the domain of (f)/(g).