Question

Select the interval where f(x) > 0 for the function f(x).

f(x) = -2 if -2 < x < -1
f(x) = -1 if -1 < x < 0
f(x) = 1 if 0 < x < 1
a) -2 < x < -1
b) -1 < x < 0
c) 0 < x < 1
d) 1 < x < 2

Answer 1

The function f(x) is greater than zero only in the interval given by option c) 0 < x < 1. This is based on the provided definitions of the function f(x) for various intervals.

Step-by-step explanation:

The question asks us to select the interval where the function f(x) is greater than zero. According to the function definitions given, f(x) has different values in different intervals. To find where f(x) > 0, we simply look at the values of f(x) provided for each interval:

• f(x) = -2 if -2 < x < -1, so in this interval f(x) is not greater than 0.
• f(x) = -1 if -1 < x < 0, so in this interval f(x) is also not greater than 0.
• f(x) = 1 if 0 < x < 1, so in this interval f(x) is greater than 0.
• There's no provided value for f(x) if 1 < x < 2, hence this option is not applicable.

Therefore, the correct answer is option c) 0 < x < 1, where the function f(x) is indeed greater than zero.