SOLUTION: how to find the inverse and domain of f(x) = (3x)/(sqrt(6x^2-12))

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Question 984822: how to find the inverse and domain of f(x) = (3x)/(sqrt(6x^2-12))
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The INVERSE relation, %283y%2Fsqrt%286y%5E2-12%29%29=x

9y%5E2%2F%286y%5E2-12%29=x%5E2

%283y%5E2%29%2F%282y%5E2-4%29=x%5E2

3y%5E2=2xy%5E2-4x%5E2

3y%5E2-2xy%5E2=-4x%5E2

2xy%5E2-3y%5E2=4x%5E2

%28y%5E2%29%282x-3%29=4x%5E2

y%5E2=%284x%5E2%29%2F%282x-3%29

y=0%2B-+sqrt%284x%5E2%29%2Fsqrt%282x-3%29, two parts. Upper part and a lower part.

y=0%2B-+%282x%29%2Fsqrt%282x-3%29

highlight%28y=0%2B-+2x%2Asqrt%282x-3%29%2F%282x-3%29%29, still this inverse relation is two parts.
Domain is x%3E=3%2F2. Each branch depends on which one of the branches of the original function is used.

graph%28300%2C300%2C-2%2C10%2C-3%2C9%2C2x%2Asqrt%282x-3%29%2F%282x-3%29%29

graph%28300%2C300%2C-2%2C10%2C-9%2C3%2C-2x%2Asqrt%282x-3%29%2F%282x-3%29%29