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139
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
139
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(x) = √(3x + 1), demonstrating the step-by-step algebraic process.
Another example shows how to find the inverse of g(x) = (x - 3) / (x + 2), 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^(-1)(x), reflect the graph of y = f(x) 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.
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)) = g(f(x)) = x
A step-by-step example is provided to show that f(x) = 4x-1 and g(x) = (x+1)/4 are inverse functions.
The page then outlines the algebraic method for finding inverse functions:
Highlight: The inverse of f(x) is denoted as f^(-1)(x).
An example is given to find the inverse of f(x) = 5x + 4 and determine its domain.
Vocabulary: Domain refers to the set of possible input values for a function.
20
610
12/13
Integration Cheat Sheet
AQA A Level maths pure revision sheet covering the integrals of a range of different functions.
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S5
Wave Function notes
notes for higher maths on the wave function
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142
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Key points for OCRMEI ALevel Maths
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Exact trig values
the exact trig values with a written example of how you could used it in a question.
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Edexel Maths Large Data Set
A summary covering everything included in the Edexel large data set
Average app rating
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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.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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(x) = √(3x + 1), demonstrating the step-by-step algebraic process.
Another example shows how to find the inverse of g(x) = (x - 3) / (x + 2), 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^(-1)(x), reflect the graph of y = f(x) 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.
Access to all documents
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)) = g(f(x)) = x
A step-by-step example is provided to show that f(x) = 4x-1 and g(x) = (x+1)/4 are inverse functions.
The page then outlines the algebraic method for finding inverse functions:
Highlight: The inverse of f(x) is denoted as f^(-1)(x).
An example is given to find the inverse of f(x) = 5x + 4 and determine its domain.
Vocabulary: Domain refers to the set of possible input values for a function.
Maths - Integration Cheat Sheet
AQA A Level maths pure revision sheet covering the integrals of a range of different functions.
20
610
0
Maths - Wave Function notes
notes for higher maths on the wave function
3
40
0
Maths - Trigonometry
Key points for OCRMEI ALevel Maths
9
142
0
Maths - Exact trig values
the exact trig values with a written example of how you could used it in a question.
20
438
0
Maths - Edexel Maths Large Data Set
A summary covering everything included in the Edexel large data set
42
1197
0
Average app rating
Pupils love Knowunity
In education app charts in 12 countries
Students have uploaded notes
iOS User
Philip, iOS User
Lena, iOS user
