SOLUTION: Use the following function to answer all parts of the question: g(x) = 3x+1 / x-1 A.)Evaluate the function at the given values. Show complete work. ANswers must be simplified c

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Question 176548: Use the following function to answer all parts of the question:
g(x) = 3x+1 / x-1
A.)Evaluate the function at the given values. Show complete work. ANswers must be simplified completely.
i.) g(0)
ii.) g(2/3)
B.) Find x if g(x)=2
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I am getting these answers and they are not adding up:
A)
i.) -1
ii.)-9
B) 2
Thank you for your help!
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!
Is the function g%28x%29=%283x%2B1%29%2F%28x-1%29 ???

A)

i)

g%28x%29=%283x%2B1%29%2F%28x-1%29 Start with the given function.


g%280%29=%283%280%29%2B1%29%2F%280-1%29 Plug in x=0


g%280%29=%280%2B1%29%2F%280-1%29 Multiply


g%280%29=%281%29%2F%28-1%29 Combine like terms.


g%280%29=-1 Reduce. So you are correct.


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ii)

g%28x%29=%283x%2B1%29%2F%28x-1%29 Start with the given function.


g%282%2F3%29=%283%282%2F3%29%2B1%29%2F%282%2F3-1%29 Plug in x=0


g%282%2F3%29=%282%2B1%29%2F%282%2F3-1%29 Multiply


g%282%2F3%29=%283%29%2F%28-1%2F3%29 Combine like terms.


g%282%2F3%29=%283%29%28-3%2F1%29 Flip the second fraction and multiply


g%282%2F3%29=-9 Multiply and simplify. Again, you are correct.



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B)

g%28x%29=%283x%2B1%29%2F%28x-1%29 Start with the given function.


2=%283x%2B1%29%2F%28x-1%29 Plug in g%28x%29=2


2%28x-1%29=3x%2B1 Multiply both sides by x-1.


2x-2=3x%2B1 Distribute.


2x=3x%2B1%2B2 Add 2 to both sides.


2x-3x=1%2B2 Subtract 3x from both sides.


-x=1%2B2 Combine like terms on the left side.


-x=3 Combine like terms on the right side.


x=%283%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-3 Reduce.


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Answer:

So the answer is x=-3


In other words, when x=-3 then g%28x%29=2. So this means that g%28-3%29=2