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For what values of x is f(x) - g(x) positive?

For what values of x is f(x) - g(x) positive?-example-1
User Plum
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1 Answer

4 votes

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).

User Richard Hansell
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