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https://math.answers.com/algebra/Do_all_functions_have_inverses_If_no_which_ones_do

Do all functions have inverses If no which ones do? - Answers

No. 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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Do all functions have inverses If no which ones do? - Answers

https://math.answers.com/algebra/Do_all_functions_have_inverses_If_no_which_ones_do

No. 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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https://math.answers.com/algebra/Do_all_functions_have_inverses_If_no_which_ones_do

Do all functions have inverses If no which ones do? - Answers

No. 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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      No. 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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