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Inverse function

If  to change an argument and a function by roles, then  x will be a function of  y. In this case we say about a new function, called an inverse function. Assume, we have a function:

v = u 2 ,

where  u  is an argument and  v  is a function. If to change them by roles, we’ll receive  u  as a function of  v :

If  to mark in both of the functions an argument as  x and a function as y, then we have two functions:

each of which is an inverse one to another.

E x a m p l e s . These functions are inverse one to another:

                         1)  sin x  and  Arcsin x,  because if  y = sin x,  then  x = Arcsin y;
                         2)  cos and  Arccos x,  because if  y = cos x,  then  x = Arccos y;
                         3)  tan x  and  Arctan x,  because if  y = tan x,  then  x = Arctan y;
                         4)  e x  and  ln x,  because if  y = e x,  then  x = ln y.


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