Answer:
Option D
The domain of the function is: {4, 7}
Step-by-step explanation:
We know that for polynomial functions like its domain and its rank are all real numbers. However, for this case we are told that the function range is: the set {25, 64}
This means that the function is bounded.
Then the domain of f(k) are all possible values of k such that f(k) belongs to the interval {25, 64}.
To find the limit values of k then we do f(k) = 25
Now we factor the expression:
Then k = 4 and k = -6.
Now we do f(k) = 64
We factor the expression:
k = -9 and k = 7.
Finally we search between the options given an interval that matches.
The option that matches is option D {4, 7}