Answer:
(0, 4)
Explanation:
The statement f(x) - g(x) is positive can also be written as an inequality:
f(x) - g(x) > 0
We can add g(x) to both sides to get f(x) > g(x). This means that whenever the value of f(x) is greater than g(x), the value of the f(x) - g(x) is positive. Graphically, this is when the graph of f(x) is above the graph of g(x) for a given x value.
Looking at the graphs, it is apparent that f(x) > g(x) from 0 to 4, which is where they cross. Notice that during this period, f(x) is above g(x).
Since the points at x = 0, 4 would be where f(x) - g(x) is 0 (since both functions yield the same value), they would not be included as 0 is not positive.
Therefore, the answer would be 0 < x < 4 or in interval notation: (0, 4).