Hi guys! I’m Nancy and I’m going to show you how to find the inverse of a function. What’s an inverse? An inverse is just the reverse of a function. It basically undoes whatever your function did. So if your function takes X and gives you Y your inverse function is taking that Y and giving you back X. Why would you want to do this? Good question. I don’t know! but your teacher wants you to so let me show you how to find the inverse function. So what you’ll already need to know is how to tell if something is a 1 to 1 function. So for every X value you only have one corresponding Y value. OK. So say you have a function like this f(x)=(x + 2) / x. and you need to find the inverse if it exists. Of course for this function we also need to keep in mind that X cannot equal zero. because we can’t divide by zero. The first step Is just to rewrite f(x) as just Y. So we would just have Y equals (x + 2) / x. Then this is the most important step you need to swap X and Y. So you switch X and Y everywhere they appear. So we would actually have X on the left side instead of Y. Here on the right side replace X with Y everywhere. So we would have (y + 2) / y. Last step you need to solve for Y. so that we’re back to Y equals with Y alone on the left side. To do that we’ll need to clear this fraction. So you would multiply both sides by Y to clear the fraction. and then get in the next line (x * y)=just (y + 2). because we’ve cleared the Y. Then if you want to get Y alone you’ll need to have all your Ys on one side. Why don’t we just bring this Y over to the left by subtracting it from both sides. So you get (x * y) – y=2 Now to solve for Y you only want Y to appear once on the left side. The best way to do that is to factor out a Y. So you’d have y( and what’s left is x – 1=2. Final step Divide out the (x – 1) from both sides. So you have y=2 / (x – 1) To write this as a function we would use inverse notation. finverse (with a -1 superscript) of X equals the expression. But first you have to check this is actually a function. Sometimes it’s just a relation and not a function. Is this a function? It is because for any one X value we plug in there’s only one corresponding Y. And if we look at the graph of this function as you know it would look something like this. So if you did the vertical line test and checked everywhere it only intersects once. So it’s a function. So we can use this notation. f inverse (x)=2 / (x – 1) If you found that it’s not a function you would just answer “inverse function does not exist”. So your answer for the inverse function is f inverse (x)=2 / (x – 1) So this one magically worked out. But some things to look out for where you may not have an inverse function and your inverse function doesn’t exist is if you have a y^2 somewhere here in your equation. Or you have a graph that could look something like this. Where if you drew a vertical line it would cross more than once. Might cross twice. You wouldn’t have a function in that case. So you wouldn’t have an inverse function. and you would just say “the inverse function doesn’t exist”. I hope this video helped you understand how to find the inverse of a function. If it exists. If it did help you please click “like”!