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If \(f(x) = \frac{x}{2x - 3}\), then find \(f^{-1}(x)\)

 Jul 29, 2020
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To find the inverse of a function, you first need ot swap in "y" for the "f(x)"

Then, we need to switch the x for the y and vice versa.

Then, solve for the y.

(you can read more about it on https://www.coolmath.com/algebra/16-inverse-functions/05-how-to-find-the-inverse-of-a-function-01.)

Okay, lets try it with your values:

 

First, we need to swap in the y for the f(x). So:

\(y=\frac{x}{2x-3}\)

Swap the x for the y, and we get:

\(x = \frac{y}{2y-3}\)

Now, let's test your algebra. Can you solve for y? 

Once you have done that, the inverse is in your equation!

 Jul 29, 2020

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