invfunc - Maple Help

invfunc

Inverse Function Table

 Calling Sequence invfunc[f] Invfunc[f]

Parameters

 f - function name

Description

 • The invfunc table is used by solve, simplify and the @@ operator to replace (explicit or implicit) occurrences of expressions of the form ${f}^{\left(-1\right)}$ with the corresponding inverse function.
 • The Invfunc table is similar to the invfunc table, but returns a multiple valued inverse (in case the inverse is a multiple valued function). A multiple value function normally uses a _Z or _NN additional variable which is assumed to be in the correct domain. _Zxx variables stand for arbitrary integers, _NNxx stand for arbitrary natural numbers (non-negative integers).
 • Entries may be added to or deleted from the table just as for any other Maple table.
 • The table is uni-directional.  That is, if there is an entry in the table of the form invfunc[f] = g, Maple does not assume that ${g}^{\left(-1\right)}=f$.

Examples

 > sin@@(-1);
 ${\mathrm{arcsin}}$ (1)
 > ln@@(-3);
 ${{\mathrm{exp}}}^{\left({3}\right)}$ (2)
 > LambertW@@(-1);
 ${\mathrm{invfunc}}\left[{\mathrm{LambertW}}\right]$ (3)
 > unprotect('invfunc');
 > invfunc[f] := g;
 ${{\mathrm{invfunc}}}_{{f}}{≔}{g}$ (4)
 > f@@(-2);
 ${{g}}^{\left({2}\right)}$ (5)
 > solve(LambertW(x)=y, x);
 ${y}{}{{ⅇ}}^{{y}}$ (6)
 > Invfunc[sin](1);
 $\frac{{1}}{{2}}{}{\mathrm{\pi }}{+}{2}{}{\mathrm{\pi }}{}{\mathrm{_Z1~}}$ (7)
 > Invfunc[exp](x);
 ${\mathrm{ln}}{}\left({x}\right){+}{2}{}{I}{}{\mathrm{\pi }}{}{\mathrm{_Z2~}}$ (8)