Question

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

Answer 1

9514 1404 393

Answer:

f^-1(x) = 2x/(x -1)

Explanation:

You can find the inverse function by solving for y:

`f(y)=x\\\\(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=(2x)/(x-1) \qquad\text{divide by the coefficient of $y$}\\\\\boxed{f^(-1)(x)=(2x)/(x-1)} \qquad\text{in functional form}`