 To finish our discussion about inverse functions, let's provide one very basic example of why, an application, why someone would care about inverse functions in the first place. So we're familiar with the concept of temperature. There's two very common ways of measuring temperature. Here in the United States, Fahrenheit is the most common measurement for temperature. And basically everywhere else in the world, Celsius is the most common way of measuring temperature. And Lord Kelvin is just rolling over his grave somewhere because there's another way of doing temperature that we won't mention at this moment whatsoever. But if you were interested in converting, like let's say you went on a trip to England, right? Where they're measuring temperature in Celsius, you might be like, okay, it's 15 degrees outside. Celsius is that hot, is that cold? If you don't know, if you don't know, then you don't know how to dress. So I'd be wearing a jacket, should I be wearing a coat? I don't know. Or if you are visiting the United States and you're from England, right? You might be like, oh, it's 70 degrees outside. Is that hot, is that cold? I don't know. So we have to oftentimes convert between different units. And so you often see equations like this. This equation right here shows us how to convert from Fahrenheit into Celsius here because we can insert the Fahrenheit into the equation and then simplify the expression to get us C, right? That's exactly what we would do. Now, if we wanted to compute a formula that converts Celsius to Fahrenheit, we wanna reverse this process right here, which is exactly what the inverse function's all about. So if you want to have a formula that converts Celsius to Fahrenheit without having to ask Alexa or Siri to help you out here, it just means take this formula and solve for F. So to start off, you'll times both sides by nine-fifths. What's good for the goose is good for the gander. F minus 32 is equal to nine-fifths C. Add 32 to both sides and you get Fahrenheit is equal to nine-fifths C plus 32. And so we can then see right here that from the formula that converts Fahrenheit to Celsius, we can find a formula that converts Celsius to Fahrenheit. And this is exactly the inverse operation. And so if you were to check, oh, it's zero degrees Celsius outside, you plug that into the equation right here and you would see that it's 32 degrees Fahrenheit. That's a simple conversion, but that's one I'll point out there. That's a nice number here because that's the freezing point of water. But I hope this example is enough to illustrate one of the many ways we use inverse functions. This is a very important calculation we've talked about in lecture seven and eight in a series. And this is something we'll have to be doing a lot. Every time we solve an equation, we are essentially computing an inverse function. And once we have the inverse function, we potentially can then expedite solving equations in the future using that inverse relationship. That's gonna end our lecture eight. And so ends chapter one in our series about fundamentals of functions. In the forthcoming chapters, we're gonna be focusing on specific function families. In chapter two, for example, we'll be focusing on linear functions, their graphs, applications and such. Chapter three, we'll move on to quadratic functions. We'll be looking at story problems involving quadratic inequalities, equations, all of that jazz, and we'll keep on going. We'll keep on going like that in the future. So thanks for watching this video here today. If you learned something, hit the like button. If you wanna learn some more about cool math concepts in the future, feel free to subscribe. And if ever you have any questions, please post them in the comments below and I'd be glad to answer them for you. See you next time, everyone. Bye.