Question

What is the inverse function of f(x) = x/x-2

Answer 1

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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:

  $f(y)=x\\\\\dfrac{y}{y-2}=x\\\\x(y-2)=y \qquad\text{multiply by y-2 }\\\\xy-2x=y \qquad\text{eliminate parentheses}\\\\xy-y=2x \qquad\text{add 2x-y }\\\\y(x-1)=2x \qquad\text{factor}\\\\y=\dfrac{2x}{x-1} \qquad\text{divide by the coefficient of y }\\\\\boxed{f^{-1}(x)=\dfrac{2x}{x-1}} \qquad\text{in functional form}$