Inverse function for several variables

  • #1
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Main Question or Discussion Point

in one dimension one have that for a function [tex] f(x) [/tex] we can define another function [tex] g(x) [/tex] so [tex] f(g(x)=x [/tex]

my question or problem is the following, if i have a function of three variables [tex] f(x,y,z) [/tex] then i can define another function [tex] g(x,y,z) [/tex] so [tex] f(g(x,y,z))=Id [/tex]

for example for the function [tex] f(x,y,z)= xyz [/tex] what would be its inverse g??
 

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  • #2
LCKurtz
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in one dimension one have that for a function [tex] f(x) [/tex] we can define another function [tex] g(x) [/tex] so [tex] f(g(x)=x [/tex]

my question or problem is the following, if i have a function of three variables [tex] f(x,y,z) [/tex] then i can define another function [tex] g(x,y,z) [/tex] so [tex] f(g(x,y,z))=Id [/tex]

for example for the function [tex] f(x,y,z)= xyz [/tex] what would be its inverse g??
It doesn't have an inverse because it is not 1-1 onto any point any point in its range. For example if d = abc then d also equals bac, cba etc.
 

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