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Is there any function that is equal to its own inverse?
Yes. If then and we can think of several functions that have this property. The identity function does, and so does the reciprocal function, because
Any function where is a constant, is also equal to its own inverse.
Access these online resources for additional instruction and practice with inverse functions.
Visit this website for additional practice questions from Learningpod.
Describe why the horizontal line test is an effective way to determine whether a function is one-to-one?
Each output of a function must have exactly one output for the function to be one-to-one. If any horizontal line crosses the graph of a function more than once, that means that -values repeat and the function is not one-to-one. If no horizontal line crosses the graph of the function more than once, then no -values repeat and the function is one-to-one.
Why do we restrict the domain of the function to find the function’s inverse?
Can a function be its own inverse? Explain.
Yes. For example, is its own inverse.
Are one-to-one functions either always increasing or always decreasing? Why or why not?
How do you find the inverse of a function algebraically?
Given a function solve for in terms of Interchange the and Solve the new equation for The expression for is the inverse,
Show that the function is its own inverse for all real numbers
For the following exercises, find for each function.
For the following exercises, find a domain on which each function is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of restricted to that domain.
Given and
a. and b. This tells us that and are inverse functions
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