 This video is part one of discussing inverses. So inverses, you perform an inverse every day when you undo something. For example, if you take your coat off a hanger and put it on, this can be undone. So let's do the steps to see what we can do when we have a function and it's inverse. So if we think about our function as putting on a coat, it's on a hanger. So the first thing that we have to do is take it off the hanger. And then the second thing that we're gonna do is that we are going to get your arms in the coat. And then the last step that you're gonna do, my son said, well, you check outside to see what the weather's gonna be like to side if you're gonna zip it up or not. But I always zip my nut because I'm always cold. So I would zip it. So then the inverse of that, think about what do you do when you take off your coat, when you come home and you're ready to relax? Well, you unzip your coat because it's zipped. Then you take your arms out so you can take it off, out. And then, unless you're my children, you put it on the hanger. So what can you say about the order of the steps in the function F of C and the inverse function F inverse of C? You can say that the order is the opposite order. And you could also say, along with order, we could also say that it's the opposite actions. And I want you to notice here that it says that inverse function, F to the negative first C, doesn't mean F to the negative one power. It looks like F to the negative one. But you'll notice I was saying F inverse of C. That's the way that's read, F inverse of C. So let's do some math. If you add in each of your numbers, what is the inverse? You would subtract two. If you wanted to undo adding two, you would subtract two. If you divide any number by negative three, what is the inverse? Well, the inverse would be to multiply. And you would multiply by negative three. You undo with the same thing. Notice when we go back and think about the code in the hanger, I didn't put it on something else. I put it on the hanger, just like I had taken it off the hanger. So we keep the negative three, but we multiply instead of divide. So it's the operation that we need to be the opposite. What is the word of operations for this function? Remember, gemdust, you got your grouping symbols, exponents, multiply, divide, add, and subtract. So the first thing we do to this X is that we multiply by two. So we multiply by two. And then the second thing we do is to subtract the five. So let's the inverse order of operations for the inverse. Remember with the code in the hanger, we started with the last thing. I zipped my code up, the last thing in the function, but I unzipped it in the inverse function. So I'm going to add, do the opposite operation, my five. And then I'm going to not multiply by two, but divide by two. So that means that I start with my X and I add five to it. That's the first step. And then from there, I'm going to divide by two. And you have to divide everything you've done so far by two. So X plus five all over two would be my function, my inverse function. Let's do one more. Again, what's the order of operations? Let's list those operations. So I've got this X. The first thing I would do is inside the grouping symbol. So I would subtract six first. And then after I've subtracted the six, I would square or care it to by my shorthand. So the inverse operations, the opposite of squaring would be to take the square root. And then the opposite of six would be, or subtracting six would be to add six. So remember it's reverse order, reverse operation. Start with the last thing and make that your first, but do the opposite. And then work your way backward. So we start with X. And the first thing we have to do is take the square root of X. And then it says plus six. I've already taken the square root of six, so the plus six goes outside the radical. So the Fn versus equal to the square root of X plus six.