Determining the inverse function operation from a function definition

Hi.
I am working on a small project to evaluate and execute unit conversion
expressions. I started wondering whether it was possible to determine what
the reverse conversion rules might blook like.


For example, one might want to define the classic Celsius to Fahrenheit
convesrion expression along the lines of:


F( c ) = ( 9 / 5 ) * c + 32.


It seems as though there's enough information there to deduce the inverse
Fahrenheit to Celsius conversion:


C( f ) = ( f - 32 ) / ( 5 / 9 )




It "feels" as though the inverse operation could be accomplished by
backing-out the original operation steps in reverse order, but it appears
that such an approach could also be fraught with peril.


The problem appears to lie in the domain of ( one to one ) function
inversion or maybe equation solving.


I presume that such an algorithm has been implemented a hundred or so times,
but my research is coming up dry.


I'd appreciate it if someone could point me to some relevant material.


TIA

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