Graphs Of A Function And Its Inverse
Akopọ
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 \(y = x\).
Awọn Afojusun
- 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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Oriire fun ipari ẹkọ lori Graphs Of A Function And Its Inverse. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
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- 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
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Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
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Abala ìwé ẹ̀kọ́
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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