Final answer:
A function with a horizontal line graph, like f(x), where x is between 0 and 20 and f(x) is constant, is indeed a function. When F in equations A × F = B × F is not zero, A can be concluded to equal B. The probability P (0 < x < 12) for a constant function f(x) equal to 12 throughout its domain is 1.
Step-by-step explanation:
To determine if f is a function from the given condition, we need to analyze the given statements. A function must assign exactly one output for each input within its domain. Since the graph of f(x) represents a horizontal line within the range 0 ≤ x ≤ 20, then f is constant and indeed a function because every x value has a unique f(x).
Regarding the equation A × F = B × F, we can conclude A = B only if F is not zero, because cancelling out F from both sides of the equation will yield A = B. For the equation A FB F, we cannot conclude A = B without additional context. Finally, if FÃ = BF and F is not zero, we can indeed conclude A = B.
The question about the continuous probability function f(x) equal to 12 from 0 ≤ x ≤ 12 asks for the probability P (0 < x < 12). Since f(x) is a constant function, the probability would simply be 1 because the event is certain within this interval.