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User EdeDJ
31/08/2022
Maths
Inverse Functions notes
Inverse Functions in Higher Mathematics: A Comprehensive Guide
This guide explores the concept of inverse functions in higher mathematics, covering their definition, properties, and methods for finding them. It provides detailed explanations, examples, and graphical representations to help students understand this crucial topic.
31/08/2022
143
This page delves deeper into finding inverse functions for more complex equations and explores their graphical representations.
The page begins with an example of finding the inverse of f = √, demonstrating the step-by-step algebraic process.
Another example shows how to find the inverse of g = / , which involves more complex algebraic manipulation.
Highlight: A function only has an inverse if it is a one-to-one function, meaning for every input there is exactly one output.
The page concludes with a discussion on graphing inverse functions:
Definition: To find the graph of y = f^, reflect the graph of y = f in the diagonal line y = x.
A visual representation is provided to illustrate this concept, showing the original function and its inverse reflected across the line y = x.
Example: The graph shows how the original function and its inverse are symmetrical about the line y = x.
This comprehensive guide provides students with a solid foundation in understanding and working with inverse functions in higher mathematics.
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Inverse Functions in Higher Mathematics: A Comprehensive Guide
This guide explores the concept of inverse functionsin higher mathematics, covering their definition, properties, and methods for finding them. It provides detailed explanations, examples, and graphical representations to help students understand... Show more
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This page delves deeper into finding inverse functions for more complex equations and explores their graphical representations.
The page begins with an example of finding the inverse of f = √, demonstrating the step-by-step algebraic process.
Another example shows how to find the inverse of g = / , which involves more complex algebraic manipulation.
Highlight: A function only has an inverse if it is a one-to-one function, meaning for every input there is exactly one output.
The page concludes with a discussion on graphing inverse functions:
Definition: To find the graph of y = f^, reflect the graph of y = f in the diagonal line y = x.
A visual representation is provided to illustrate this concept, showing the original function and its inverse reflected across the line y = x.
Example: The graph shows how the original function and its inverse are symmetrical about the line y = x.
This comprehensive guide provides students with a solid foundation in understanding and working with inverse functions in higher mathematics.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the concept of inverse functions and provides methods for identifying and finding them.
Definition: Inverse functions are functions that reverse the effect of each other.
The identity function is used to demonstrate that two functions are inverse functions:
Example: f) = g) = x
A step-by-step example is provided to show that f = 4x-1 and g = /4 are inverse functions.
The page then outlines the algebraic method for finding inverse functions:
Highlight: The inverse of f is denoted as f^.
An example is given to find the inverse of f = 5x + 4 and determine its domain.
Vocabulary: Domain refers to the set of possible input values for a function.
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very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
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This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
