Question 707097
That is usually not its meaning for functions.  Similar notation but with different meaning for a number than for a function.  


a is a real number.  There is a number which if multiplied by a gives the product, 1.  {{{a(a^-1)=1}}}, and we say that {{{a^-1}}} is the multiplicative inverse of a.


g(x) is a function which uses the independant variable number, x.  This means you give the function a number or a value as input and g is then evaluated at that given input.  There is another function which will undo what g(x) does and give you x as the result.  Call this new function, {{{g^-1(x)}}}.  This is the inverse of g(x).  It does NOT mean {{{1/(g(x))}}}.  What we have with these two inverse functions is that {{{g(g^-1(x))=x}}}, and {{{g^-1(g(x))=x}}}.  


[the little operator dot in the above typeset expressions were unintended.  Books usually permit a much better job of this.]