




A function has another function as inverse if each of its values occur only once.
Otherwise, if say f(a) = y and f(b) = y, we have a problem deciding if f^{  1}(y) = a or f ^{ 1}(y) = b.
Thus x^{2} = y^{2} is satisfied by x = y and x = y.
We can resolve this difficulty if it occurs by defining the inverse to be some specific value that obeys our conditions.
This is what we do for the square root._{ } is the positive square root but  is also a square root of x. Thus the "square" has a twovalued inverse.
In the example above, we would have f^{1}(y) = a and also b.
If you want to define a singlevalued function f ^{ 1}, you must add another condition. For the function , that condition is .