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Does f have an inverse? - Answers

It very much depends on f. If f is one-to-one and onto (injective and surjective) then yes, else no. One-to-one means that for each element in the domain there is a different image in the range. This is not true for g(x) = x2 for example, where -3 and +3 are both mapped to +9. So g(x) does not have an inverse UNLESS you restrict the domain of g to non-negative reals. Then -3 is no longer in the domain. Onto means that every element in the range of the function has a corresponding element in the domain which is mapped onto it. Again, a suitable changes to the domain and range can transform a function without an inverse into an invertible one.



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Does f have an inverse? - Answers

https://math.answers.com/math-and-arithmetic/Does_f_have_an_inverse

It very much depends on f. If f is one-to-one and onto (injective and surjective) then yes, else no. One-to-one means that for each element in the domain there is a different image in the range. This is not true for g(x) = x2 for example, where -3 and +3 are both mapped to +9. So g(x) does not have an inverse UNLESS you restrict the domain of g to non-negative reals. Then -3 is no longer in the domain. Onto means that every element in the range of the function has a corresponding element in the domain which is mapped onto it. Again, a suitable changes to the domain and range can transform a function without an inverse into an invertible one.



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https://math.answers.com/math-and-arithmetic/Does_f_have_an_inverse

Does f have an inverse? - Answers

It very much depends on f. If f is one-to-one and onto (injective and surjective) then yes, else no. One-to-one means that for each element in the domain there is a different image in the range. This is not true for g(x) = x2 for example, where -3 and +3 are both mapped to +9. So g(x) does not have an inverse UNLESS you restrict the domain of g to non-negative reals. Then -3 is no longer in the domain. Onto means that every element in the range of the function has a corresponding element in the domain which is mapped onto it. Again, a suitable changes to the domain and range can transform a function without an inverse into an invertible one.

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      It very much depends on f. If f is one-to-one and onto (injective and surjective) then yes, else no. One-to-one means that for each element in the domain there is a different image in the range. This is not true for g(x) = x2 for example, where -3 and +3 are both mapped to +9. So g(x) does not have an inverse UNLESS you restrict the domain of g to non-negative reals. Then -3 is no longer in the domain. Onto means that every element in the range of the function has a corresponding element in the domain which is mapped onto it. Again, a suitable changes to the domain and range can transform a function without an inverse into an invertible one.

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