a. Yes, there are multiple values of x at which the equation f(x) = g(x) is true.
b. Here are two values of x at which the inequality f(x) > g(x) is true:
- x ≈ 1: Observing the graph, we see that the f(x) curve is above the g(x) curve between x = 0 and approximately x = 4. Therefore, f(x) > g(x) for this range of values, including x ≈ 1.
- x ≈ 11: Similarly, the f(x) curve is above the g(x) curve between approximately x = 9 and x = 12. Therefore, f(x) > g(x) for this range, including x ≈ 11.
a. Finding points where f(x) = g(x):
Yes, there are several values of x at which the equation f(x) = g(x) is true. We can see from the graph that the two lines intersect at three points:
- Approximately x = 4: At this point, both curves have a y-value of around 3.5.
- Approximately x = 7: Here, both curves have a y-value of around 4.75.
- Approximately x = 9.5: At this intersection, the y-value is roughly 7.5.
Therefore, these three x-values satisfy the equation f(x) = g(x).
b. Identifying points where f(x) > g(x):
Finding values where f(x) > g(x) requires examining the relative positions of the curves. Here are two examples of x-values where this inequality holds:
- x ≈ 1.5: Between x ≈ 0 and x ≈ 4, the f(x) curve consistently stays above the g(x) curve. Therefore, f(1.5) > g(1.5).
- x ≈ 11: Similarly, from around x ≈ 9 to x ≈ 12, the f(x) curve remains above the g(x) curve. So, f(11) > g(11).
Remember, these are just two examples, and several other x-values within the given range satisfy the inequality f(x) > g(x).