Answer:
B
Step-by-step explanation:
To find (f/g)(x), you have to divide f(x) by g(x). To make division easier, factor out the equations given as much as possible.
f(x) = 3x + 5 Factored
g(x) = 3x² - x - 10
g(x) = (3x + 5)(x - 2) Factored
Divide the two equations.
[tex](f/g)(x)=\frac{3x + 5}{(3x + 5)(x-2)} \\(f/g)(x)=\frac{1}{x-2}[/tex]
The denominator of a fraction can never be zero. It can be positive and negative numbers, but not zero. Since the x is in the denominator, the domain cannot include a number that causes the denominator to be zero. The number that would cause x to be zero is 2, meaning that it can not be included in the domain.
x - 2 ≠ 0
(x - 2) + 2 ≠ 0 + 2
x ≠ 2
This means that the answer is B.
