Question

Find the domain of y=2/3x-1 if the range is {-3, -1, 7, 17}.

Answer 1

Answer: The domain is {-3, 0, 12, 27}

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Explanation:

First solve for x to get

y = (2/3)x - 1

y+1 = (2/3)x

(2/3)x = y+1

x = (3/2)*(y+1)

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Now plug the values given into y. Do so one at a time. Lets plug in y = -3

x = (3/2)*(y+1)

x = (3/2)*(-3+1)

x = 1.5*(-2)

x = -3

So the domain value x = -3 corresponds to the range value y = -3.

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Repeat for y = -1

x = (3/2)*(y+1)

x = (3/2)*(-1+1)

x = 1.5*0

x = 0

The domain value x = 0 corresponds to the range value y = -1

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Repeat for y = 7

x = (3/2)*(y+1)

x = (3/2)*(7+1)

x = 1.5*8

x = 12

The domain value x = 12 corresponds to the range value y = 7

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Repeat for y = 17

x = (3/2)*(y+1)

x = (3/2)*(17+1)

x = 1.5*18

x = 27

The domain value x = 27 corresponds to the range value y = 17

Answer 2

Just as the domain is the x values, the range is the y values. To null out any confusion, "y" is the same as "f(x)", if that is the notation you are using.

For each range value -3, -1, 7, and 17, we will have an x-value. To find the corresponding x to each y-value, we just plug in the range for y, one at a time, and solve for x.

Try it.