Invert Command

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)]] and Invert[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.