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In general, a function f (from set A to set B) has an inverse if, for any elements a and b in A [f(a) and f(b) in B],

f(a) = f(b) imples that a = b.

Strictly speaking then, y = x2 does not have an inverse because each value of x2 (except 0) maps on to 2 distinct values of y. This does not accord with the definition of a function.

For example, f(-2) = f(2) = 4

but -2 is not 2 so sqrt is technically NOT a function.

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15y ago

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Q: Do all functions have inverses If no which ones do?
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