```Question 176548
Is the function {{{g(x)=(3x+1)/(x-1)}}} ???

A)

i)

{{{g(0)=(3(0)+1)/(0-1)}}} Plug in {{{x=0}}}

{{{g(0)=(0+1)/(0-1)}}} Multiply

{{{g(0)=(1)/(-1)}}} Combine like terms.

{{{g(0)=-1}}} Reduce. So you are correct.

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ii)

{{{g(2/3)=(3(2/3)+1)/(2/3-1)}}} Plug in {{{x=0}}}

{{{g(2/3)=(2+1)/(2/3-1)}}} Multiply

{{{g(2/3)=(3)/(-1/3)}}} Combine like terms.

{{{g(2/3)=(3)(-3/1)}}} Flip the second fraction and multiply

{{{g(2/3)=-9}}} Multiply and simplify. Again, you are correct.

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B)

{{{2=(3x+1)/(x-1)}}} Plug in {{{g(x)=2}}}

{{{2(x-1)=3x+1}}} Multiply both sides by {{{x-1}}}.

{{{2x-2=3x+1}}} Distribute.

{{{2x=3x+1+2}}} Add {{{2}}} to both sides.

{{{2x-3x=1+2}}} Subtract {{{3x}}} from both sides.

{{{-x=1+2}}} Combine like terms on the left side.

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

{{{x=(3)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}.

{{{x=-3}}} Reduce.

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