If the range of the function is f(x) = 5/x + 6.5 is {7, 6.83, 6.78, 6.75}, what is its domain?
A) {5, 10, 15, 20}
B) {10, 15, 18, 20}
C) {10, 15, 17, 20}
D) {10, 14, 16, 20}
E) {8, 15, 18, 22}
The x values that will give you 7, 6.68, 6.78 and 6.75.
Easiest to invert f(x) to find what those are. The way you wrote it, f(x) is ambiguous.
If y = (5/x) + 6.5, then y - 6.5 = 5/x, x/5 = 1/(y - 6.5) and x = 5/(y - 6.5)
If y = 5/(x + 6.5), then x + 6.5 = 5/y, x = (5/y) - 6.5
Whichever one is correct, plug those y values in and see which x values they correspond to. You'll probably only have to do 1 or 2 before the choice is clear.
Therefore, the best and most correct answer among the choices is the second option or letter B) {10, 15, 18, 20}. I hope it helps you.
