Graphs Of A Function And Its Inverse
Bayani Gaba-gaba
The inverse of a function undoes it, and there is a beautiful geometric link between the two: each is the mirror image of the other in the line \(y = x\). Seeing this reflection makes inverse functions intuitive rather than abstract.
In this lesson you will use sketch graphs to show the relationship between a function and its inverse, recognising that each is the reflection of the other in the line \(y = x\).
Manufura
- Use sketch graphs to show the relationship between a function and its inverse, recognising that each is the reflection of the other in the line y = x.
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Barka da kammala darasi akan Graphs Of A Function And Its Inverse. Yanzu da kuka bincika mahimman ra'ayoyi da ra'ayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- A function and its inverse are reflections of each other in the line: A. y = 0 B. x = 0 C. y = x D. y = -x Answer: C
- If (2, 4) lies on y = f(x), which point lies on y = f-inverse(x)? A. (2, 4) B. (4, 2) C. (-2, -4) D. (4, -2) Answer: B
- The inverse of f(x) = x^2 (x >= 0) is: A. x^2 B. 1/x^2 C. √x D. -x^2 Answer: C
- To sketch an inverse you reflect the graph in: A. the x-axis B. the y-axis C. the line y = x D. the origin Answer: C
- Reflecting (a, b) in y = x gives: A. (a, b) B. (b, a) C. (-a, b) D. (a, -b) Answer: B
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
Inverse Functions
Verify inverse functions.
"Algebra and Trigonometry: Inverse Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/3-7-inverse-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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