When we can express the inverse of sum of two functions for example f = f 1 + f 2 in terms of inverse of two functions ( f 1 − 1 , f 2 − 1 )?

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When we can express the inverse of sum of two functions for example   f  =      f    1    +      f    2   in terms of inverse of two functions   (      f    1          −      1        ,      f    2          −      1        )?

drumette824ed · Accepted Answer

There is no easy way to do so. (There is an obvious hard way: invert       f    1          −      1       and       f    2          −      1       to get       f    1   and       f    2  , sum these to get   f and then invert.)It can well happen that       f    1   and       f    2   are invertible but   f is not. Or that neither of       f    1   and       f    2   is invertible but   f is. And you can find an invertible function       f    1   and a non-invertible function       f    2   so that   f is invertible — and another pair of such functions       f    1   and       f    2   so that   f is not invertible.

When we can express the inverse of sum of two functions for example f = f 1 </msub

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