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For \(f(x) = \dfrac{x}{2x - 1}\) find the invese function of f(x).

 Jun 14, 2020
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The inverse function is the function that "undoes".

We can find the inverse function by setting f(x) as y and solving for x in terms of y.

\(y(2x-1)=x\)

\(2xy-y=x\)

\(y = 2xy-x\)

\( y=x(2y-1) \)

\(x=\frac{y}{2y-1}\)

So the inverse function is \(\frac{x}{2x-1}\)

 Jun 14, 2020
edited by thelizzybeth  Jun 15, 2020

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