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# help

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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 $$\frac{x}{2x-1}$$

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Jun 14, 2020
edited by thelizzybeth  Jun 15, 2020