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luna5f7iesajo
Answered

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}

Verified Answer :

nobillionaireNobley

y = 5/x + 6.5
5/x = y - 6.5
x = 5/(y - 6.5)

Domain = {5/(7 - 6.5), 5/(6.83 - 6.5), 5/(6.78 - 6.5), 5/(6.75 - 6.5)} = {5/0.5, 5/0.33, 5/0.28, 5/0.25} = {10, 15, 18, 20}

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.

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