Difference between revisions of "Invert Command"
From GeoGebra Manual
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| + | ;Invert[ <Function> ] | ||
| + | :Gives the inverse of the function. | ||
| + | :{{example|1=<div><code><nowiki>Invert[sin(x)]</nowiki></code> yields ''asin(x)''.</div>}} | ||
| + | :{{note|1=<div>The function must contain just one ''x'' and no account is taken of domain or range, for example for f(x) = x^2 or f(x) = sin(x). <br>If there is more than one ''x'' in the function another command might help you:</div> | ||
| + | ::{{example|1=<div>Both <code><nowiki>Invert[PartialFractions[(x + 1) / (x + 2)]]</nowiki></code> and <code><nowiki>Invert[CompleteSquare[x^2 + 2 x + 1]]</nowiki></code> yield the inverse functions.</div>}}}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
;Invert[ <Matrix> ] | ;Invert[ <Matrix> ] | ||
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;Invert[ <Function> ] | ;Invert[ <Function> ] | ||
:Gives the inverse of the function. | :Gives the inverse of the function. | ||
| − | :{{ | + | :{{example|1=<div> |
| − | : | + | :*<code><nowiki>Invert[(x + 1) / (x + 2)]</nowiki></code> yields ''<math>\frac{-2x + 1}{x - 1}</math>''. |
| − | + | :*<code><nowiki>Invert[x^2 + 2 x + 1]</nowiki></code> yields ''<math>\sqrt x - 1</math>''.</div>}} | |
| − | :{{note|1= | + | :{{note|1=In the [[CAS_View|CAS View]], the command also works if the function contains more than one ''x''.}} |
Revision as of 09:23, 7 June 2013
- Invert[ <Matrix> ]
- Inverts the given matrix.
- Example:
Invert[{{1, 2}, {3, 4}}]yields\begin{pmatrix} -2 & 1\\ 1.5 & -0.5 \end{pmatrix} , the inverse matrix of
\begin{pmatrix} 1 & 2\\ 3 & 4 \end{pmatrix}
.- Invert[ <Function> ]
- Gives the inverse of the function.
- Example:
Invert[sin(x)]yields asin(x).
- Note:The function must contain just one x and no account is taken of domain or range, for example for f(x) = x^2 or f(x) = sin(x).
If there is more than one x in the function another command might help you:- Example:Both
Invert[PartialFractions[(x + 1) / (x + 2)]]andInvert[CompleteSquare[x^2 + 2 x + 1]]yield the inverse functions.
CAS Syntax
- Invert[ <Matrix> ]
- Inverts the given matrix.
- Example:
Invert[{{a, b}, {c, d}}]yields\begin{pmatrix} \frac{d}{ad- bc} & \frac{-b}{ad- bc}\\ \frac{-c}{ad- bc}& \frac{a}{ ad- bc} \end{pmatrix} , the inverse matrix of
\begin{pmatrix} a & b\\ c & d \end{pmatrix}
.- Invert[ <Function> ]
- Gives the inverse of the function.
- Example:
Invert[(x + 1) / (x + 2)]yields \frac{-2x + 1}{x - 1}.Invert[x^2 + 2 x + 1]yields \sqrt x - 1.
- Note: In the CAS View, the command also works if the function contains more than one x.
