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# inverse function

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

Jul 29, 2020

#1
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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.

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