Обратная функция, свойства, график. Как найти функции обратные данным и построить график. 8-11 класс

Algebra, Grades 8-11. What is an inverse function? Does every function have an inverse function? How do you obtain the formula for an inverse function? What properties does an inverse function have? How do you graph an inverse function? Today, we'll answer these questions. If you haven't seen our lesson on "Functions in Mathematics," be sure to check it out; this lesson will be very clear to you. We'll remind you what a function is. We'll define an inverse function and outline how to obtain the inverse formula. Note that not every function has an inverse function. Using a specific example, we'll explain how to determine whether a given function has an inverse and why. We'll show you two ways to graph the inverse of a given function. We'll explain which functions are called mutually inverse. We'll examine the distinctive properties of mutually inverse functions. We'll also show you a typical OGE or USE assignment on "inverse functions." A detailed lesson plan and links to previous lessons can be found in the description below the video. 00:00 Start of the video. 00:50 Let's start with a review. Function. 01:54 Inverse function. 05:01 How to obtain the inverse correspondence formula? 07:20 Inverse functions on a graph. 10:04 Properties of inverse functions. 10:17 A short digression: inverse and mutually inverse functions. 10:44 Domain and range of mutually inverse functions. 11:43 Properties of the graphs of mutually inverse functions. 12:05 Monotonicity of mutually inverse functions. 13:19 Does every function have an inverse? 15:49 Method 1 of plotting the inverse correspondence graph. 18:20 Method 2 of plotting the inverse correspondence graph. 20:00 How to immediately plot the inverse of a given function? 10:20 PM Next lesson... You can find all our math video lessons for grades 5-11 on our channel under the "Playlists" tab:    / МатематикаотБаканчиковой  . If you're new to our channel and still have questions or want to refresh your memory on some terms and definitions, we recommend watching the following videos: Function in Mathematics. Definition. An example that EVERYONE understands.    • Что такое функция? Алгебра 7-11 класс. Фун...   Methods of defining a function. Examples.    • Способы задания функции. Алгебра 7-11 класс.   Graph of a linear function. The role of the slope in plotting a function graph.    • График линейной функции. Алгебра 7 класс   Follow us on other social media: https://rutube.ru/channel/23880910/ https://t.me/Matematika_ot_Bakanchikovoy https://vk.com/club211895160 Your opinion of our lessons is very important to us. Share your thoughts in the comments, ask questions, and we'll be happy to answer them. If you enjoyed the lesson, found it clear and useful, please help us develop the channel by liking it and sharing the link on social media with your friends, classmates, and, of course, teachers to share experiences. We wish you success in your math studies, and see you in the next lesson! #inversefunction #graphofinversefunction #inversefunctionsofdata #inversefunctionofdata #whichfunctionisinverse #findinversefunctionsofdata #definitionofinversefunction #howtofindinversefunction #graphofinversefunctionofdata #domainofinversefunction #mutuallyinversefunctions #graphsofmutuallyinversefunctions #propertiesofinversefunctions #propertiesofmutuallyinversefunctions #MathematicsByBakanchikova