Question

Let f(x) = 3x + 5 and g(x) = 3x2 - x - 10
Find (f/g)•(x) and state its domain

Answer 1

B

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.

`(f/g)(x)=(3x + 5)/((3x + 5)(x-2)) \\(f/g)(x)=(1)/(x-2)`

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.