This relationship applies to any function and it’s inverse and it should help you to understand why the 3-step process that you used earlier works for finding the inverse of any function! We will be using the following 3-step process that can be used to find the inverse of any function: If the function that you want to find the inverse of is not already expressed in y= form, simply replace f(x)= with y= as follows (since f(x) and y both mean the same thing: the output of the function): Now that you have the function in y= form, the next step is to rewrite a new function using the old function where you swap the positions of x and y as follows: This new function with the swapped X and Y positions is the inverse function, but there’s still one more step! {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/79\/Find-the-Inverse-of-a-Function-Step-1.jpg\/v4-460px-Find-the-Inverse-of-a-Function-Step-1.jpg","bigUrl":"\/images\/thumb\/7\/79\/Find-the-Inverse-of-a-Function-Step-1.jpg\/aid2912605-v4-728px-Find-the-Inverse-of-a-Function-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"

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\n<\/p><\/div>"}. The 5's cancel each other out during the process. An inverse function is a relation that maps Y onto X. Given the function \(f\left( x \right)\) we want to find the inverse function, \({f^{ - 1}}\left( x \right)\). Now let’s take a look at both lines on the same graph. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. The inverse of A is A-1 only when A × A-1 = A-1 × A = I; To find the inverse of a 2x2 matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc). We also have to explicitly specify the starting lower/upper bounds. (Easy to Print), Free Decimal to Fraction Chart (Printable PDF), Easy Guide to Adding and Subtracting Fractions with Unlike Denominators. Let’s take a further look at what that means using the last example: Below, Figure 1 represents the graph of the original function y=7x-4 and Figure 2 is the graph of the inverse y=(x+4)/7. % of people told us that this article helped them. © MashUp Math, LLC | Privacy Policy and Copyright Info | Terms of Service |Contact, Finding the Inverse of a Function Tutorial, How to Find the Inverse of a Function in 3 Easy Steps. Find the inverse of. Definition: The inverse of a function is it’s reflection over the line y=x.

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