If f(x) is increasing on the interval from x = 2 to x = 10, and if g(x) is decreasing on the interval from x = 2 to x = 10, then the function (f + g)(x) will be constant on the interval from x = 2 to x = 10.
true or false
False.
To determine whether the function (f + g)(x) is constant on the interval from x = 2 to x = 10, we need to consider the behavior of both f(x) and g(x) separately.
If f(x) is increasing on the interval from x = 2 to x = 10, it means that as x increases within this interval, the values of f(x) also increase.
On the other hand, if g(x) is decreasing on the same interval, it means that as x increases within this interval, the values of g(x) decrease.
When we add these two functions together to get (f + g)(x), the behavior of one function can influence the other. For example, if f(x) is increasing faster than g(x) is decreasing, then the sum (f + g)(x) could still be increasing on the interval. Conversely, if g(x) is decreasing faster than f(x) is increasing, then the sum (f + g)(x) could be decreasing on the interval.
Therefore, we cannot determine with certainty whether (f + g)(x) will be constant without knowing more about the specific functions f(x) and g(x) and the rate at which they are increasing and decreasing within the interval from x = 2 to x = 10.