Inverse functions - Revision history

Lila at 18:33, 25 October 2021

2021-10-25T18:33:17Z

2021-10-25T18:31:36Z

Resources

2021-10-05T20:04:45Z

Resources

2021-10-05T20:03:57Z

One-to-one function

2021-10-05T20:03:14Z

2021-10-05T19:59:49Z

Inverse function

2021-10-05T19:59:15Z

2020-08-12T19:02:14Z

fixing link to go straight to pdf

2020-08-11T20:40:58Z

added inverse functions notes by professor Esparza

New page

* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Inverse%20functions/ Inverse Functions]. Written notes created by Professor Esparza, UTSA.

@@ Line 70: / Line 70: @@
 ==Licensing==
 Content obtained and/or adapted from:
-* [] under a CC BY-SA license
+* [https://en.wikibooks.org/wiki/Algebra/Functions Functions, Wikibooks: Algebra] under a CC BY-SA license

← Older revision		Revision as of 18:31, 25 October 2021
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	* [https://en.wikibooks.org/wiki/Algebra/Functions Functions], Wikibooks: Algebra		* [https://en.wikibooks.org/wiki/Algebra/Functions Functions], Wikibooks: Algebra
	* [https://en.wikibooks.org/wiki/VCE_Mathematical_Methods/Inverse_functions Inverse Functions], Wikibooks: VCE Mathematical Methods		* [https://en.wikibooks.org/wiki/VCE_Mathematical_Methods/Inverse_functions Inverse Functions], Wikibooks: VCE Mathematical Methods
		+
		+	==Licensing==
		+	Content obtained and/or adapted from:
		+	* [] under a CC BY-SA license

← Older revision		Revision as of 20:04, 5 October 2021
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Inverse%20functions/Esparza%201093%20Notes%201.7.pdf Inverse Functions]. Written notes created by Professor Esparza, UTSA.		* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Inverse%20functions/Esparza%201093%20Notes%201.7.pdf Inverse Functions]. Written notes created by Professor Esparza, UTSA.
	* [https://en.wikibooks.org/wiki/Algebra/Functions Functions], Wikibooks: Algebra		* [https://en.wikibooks.org/wiki/Algebra/Functions Functions], Wikibooks: Algebra
		+	* [https://en.wikibooks.org/wiki/VCE_Mathematical_Methods/Inverse_functions Inverse Functions], Wikibooks: VCE Mathematical Methods

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 '''Horizontal Line Test'''<br/>
 If no horizontal line intersects the graph of a function in more than one place then the function is a one-to-one function.
 ==Resources==
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Inverse%20functions/Esparza%201093%20Notes%201.7.pdf Inverse Functions]. Written notes created by Professor Esparza, UTSA.
 * [https://en.wikibooks.org/wiki/Algebra/Functions Functions], Wikibooks: Algebra

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 Example:
- <math>f(x)=\sqrt{x - 1} \,</math>
+: <math>f(x)=\sqrt{x - 1} \,</math>
- <math>x = f\left(f^{-1}(x)\right)</math>
+: <math>x = f\left(f^{-1}(x)\right)</math>
- <math>x=\sqrt{f^{-1}(x) - 1} \,</math>
+: <math>x=\sqrt{f^{-1}(x) - 1} \,</math>
- <math>x^2=\sqrt{f^{-1}(x) - 1}^2 \,</math>
+: <math>x^2=\sqrt{f^{-1}(x) - 1}^2 \,</math>
- <math>x^2=f^{-1}(x) - 1 </math>
+: <math>x^2=f^{-1}(x) - 1 </math>
- <math>f^{-1}(x)=x^2 + 1\,</math>
+: <math>f^{-1}(x)=x^2 + 1\,</math>
- The Range of <math>f(x)</math> is <math>f(x)\ge0</math>. So the Domain of <math>f^{-1}(x)</math> is <math>x \ge 0</math>.
+The Range of <math>f(x)</math> is <math>f(x)\ge0</math>. So the Domain of <math>f^{-1}(x)</math> is <math>x \ge 0</math>.
 ===One-to-one function===
 A function that for every input there exists an output unique to that input.
@@ Line 54: / Line 54: @@
 ==Resources==
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Inverse%20functions/Esparza%201093%20Notes%201.7.pdf Inverse Functions]. Written notes created by Professor Esparza, UTSA.

← Older revision		Revision as of 19:59, 5 October 2021
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−	~~==Inverse function==~~
	The function <math>g</math> is the inverse of the one-to-one function <math>f</math> if and only if the following are true:<br/>		The function <math>g</math> is the inverse of the one-to-one function <math>f</math> if and only if the following are true:<br/>
	:<math>g(f(x))=x \,</math>		:<math>g(f(x))=x \,</math>

← Older revision		Revision as of 19:02, 12 August 2020
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−	* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Inverse%20functions/ Inverse Functions]. Written notes created by Professor Esparza, UTSA.	+	* [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Inverse%20functions/Esparza%201093%20Notes%201.7.pdf Inverse Functions]. Written notes created by Professor Esparza, UTSA.