Question 217944: Find the inverse of y = (3x) / (x-2) and state the domain of the inverse.
I have tried switching the x's for y. I get stuck at this step of the problem:
{(xy)-(2x)} / 3
I've looked online for inverse help, but nothing makes sense! Everyone just says switch the x for y.
Thanks
Found 2 solutions by RAY100, scott8148:
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! starting with ,,,,,,y= (3x)/(x-2)
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Inverse is,,,,,,x=(3y)/(y-2),,,,,,,just switch x for y and vice verse
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BUT, now lets put in terms of y=?
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cross multiply ,,,,x(y-2) = 3y
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xy -2x =3y
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xy -3y =2x
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y(x-3) = 2x
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y= 2x/(x-3),,,,,,,DOMAIN is all REAL numbers except x=3
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inverses should reflect over the line y=x,,,(45 degree line)
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Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! switching x and y ___ x = (3y) / (y - 2)
dividing by x and multiplying by (y - 2) ___ y - 2 = 3y / x
dividing by y ___ 1 - (2 / y) = 3 / x
adding 1 (or x/x) ___ -2 / y = (3 + x) / x
take inverse and multiply by -2 ___ y = -2x / (3 + x)
the domain is all real numbers EXCEPT -3
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