Link: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:verifying-inverse/a/verifying-inverse-functions-by-composition
Description: WebLearn how to verify whether two functions are inverses by composing them. For example, are f(x)=5x-7 and g(x)=x/5+7 inverse functions?
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Link: https://openstax.org/books/college-algebra-2e/pages/3-7-inverse-functions
Description: WebVerify inverse functions. Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one. Find or evaluate the inverse of a function. Use the graph of a one-to-one function to graph its …
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Link: https://math.libretexts.org/Courses/Reedley_College/College_Algebra_1e_(OpenStax)/04%3A_Functions/4.06%3A_Inverse_Functions
Description: WebDec 13, 2023 · Verify inverse functions. Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one. Find or evaluate the inverse of a function. Use the graph of a one-to-one function to graph its inverse function on the same axes.
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Link: https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/06%3A_Functions/6.05%3A_Inverse_Functions
Description: WebApr 17, 2022 · Progress Check 6.24: Exploring the Inverse of a Function. Let \(A = \{a, b, c\}\), \(B = \{a, b, c, d\}\), and \(C = \{p, q, r\}\). Define. Draw an arrow diagram for each function. Determine the inverse of each function as a set of ordered pairs. (a) Is \(f^{-1}\) a function from \(C\) to \(A\)? Explain. (b) Is \(g^{-1}\) a function from \(C ...
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Link: https://www.math.toronto.edu/courses/mat237y1/20199/notes/Chapter3/S3.3.html
Description: WebThe proof of the Inverse Function Theorem We can prove the theorem using the following: Assume that \(\Sigma\) is an open subset of \(\R^n\) that contains the origin, and that \(\mathbf F:\Sigma\to \R^n\) is a function of class \(C^1\) such that \[ \mathbf F({\bf 0}) = {\bf 0}, \quad \| D\mathbf F({\bf 0}) - I\|< 1.
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Link: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/a/intro-to-inverse-functions
Description: WebIntro to inverse functions. Learn what the inverse of a function is, and how to evaluate inverses of functions that are given in tables or graphs. Inverse functions, in the most general sense, are functions that "reverse" each other. For example, here we see that function f takes 1 to x , 2 to z , and 3 to y .
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Link: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:verifying-inverse/v/verifying-function-inverses-by-composition
Description: WebVerifying inverse functions by composition (video) | Khan Academy. Google Classroom. About. Transcript. Sal composes f (x)= (x+7)³-1 and g (x)=∛ (x+1)-7, and finds that f (g (x))=g (f (x))=x, which means the functions are inverses! Questions. Tips & Thanks. Want to join the conversation? Log in. Sort by: Top Voted. Kels Rowland. 8 years ago.
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