Question

Given the following image, What is the interval in which both f (x) and g(x) are positive?

A (4, ∞)
B (1, ∞)
C (–2, ∞)
D (–∞, –2) ∪ (–2, ∞)

Answer 1

A. (4, ∞)

Explanation:

To find the intersection of the intervals where the functions f(x) and g(x) are positive, we need to identify the overlapping region.

Given:

f(x) is positive in the interval: (-∞, -2) ∪ (1, ∞)

g(x) is positive in the interval: (4, ∞)

To find the intersection, we need to find the overlapping part of these intervals.

Take the intervals one by one:

For f(x):

The interval (-∞, -2) represents all values of x less than -2, and the interval (1, ∞) represents all values of x greater than 1.

For g(x):

The interval (4, ∞) represents all values of x greater than 4.

Now, we need to find the overlapping region between f(x) and g(x).

From the intervals above, we can see that the overlapping region is the interval (4, ∞), because it satisfies both conditions: it is greater than 4 (for g(x)) and greater than 1 (for f(x)).

Therefore, the intersection of the intervals where f(x) and g(x) are positive is (4, ∞).

Hence, the correct choice is A.