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#### Published on 07 Sep 2013 | over 4 years ago

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How can you find the inverse function of any function, if it exists? The inverse function is the reverse of your original function. It undoes whatever your function did. If your function takes x and gives you y, then the inverse function takes that y and gives you back x.

How to find the inverse of a function: There are three steps to finding the inverse function, if it exists.

The first step is to replace the f(x) with just the variable y.

Second, swap the x and y variables everywhere they appear in the equation.

Third, solve for y again so that you have just "y=" on one side of the equation. If this relation is a function, you can then replace the y with the "f inverse x" notation, or f^-1(x). To know if it is a function, use the Vertical Line Test or consider the form of the equation.

Remember that in a function equation, for every x you input into the equation, there can only be one corresponding y value.
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