Question

Determine all the values for which the absolute value inequality f(x) > g(x).

A. x < -2
B. x > 0
C. -4 < x < -2
D. -4 < x < 0

Answer 1

To determine the values for the inequality f(x) > g(x), we need to consider two cases and find the range of x that satisfies the condition. The correct answer is C. -4 < x < -2, as this range satisfies the given condition.

Step-by-step explanation:

The values for which the absolute value inequality f(x) > g(x) can be determined by examining the intervals where the functions f(x) and g(x) are greater than or less than each other. To solve this type of inequality, you need to consider two cases:

1. Case 1: f(x) > 0 and g(x) < 0
2. Case 2: f(x) < 0 and g(x) > 0

In each case, the solution will be a range of values for x.

The correct answer is C. -4 < x < -2, as this range satisfies the given condition.