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Answer:
f^-1(x) = 2x/(x -1)
Step-by-step explanation:
You can find the inverse function by solving for y:
[tex]f(y)=x\\\\\dfrac{y}{y-2}=x\\\\x(y-2)=y \qquad\text{multiply by $y-2$}\\\\xy-2x=y \qquad\text{eliminate parentheses}\\\\xy-y=2x \qquad\text{add $2x-y$}\\\\y(x-1)=2x \qquad\text{factor}\\\\y=\dfrac{2x}{x-1} \qquad\text{divide by the coefficient of $y$}\\\\\boxed{f^{-1}(x)=\dfrac{2x}{x-1}} \qquad\text{in functional form}[/tex]
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