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Is every function a onto function?

Updated: 10/17/2024
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11y ago

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No. It depends on how the range is defined.

y = x2 is not onto R but can be made onto by changing the range to R0+.

No. It depends on how the range is defined.

y = x2 is not onto R but can be made onto by changing the range to R0+.

No. It depends on how the range is defined.

y = x2 is not onto R but can be made onto by changing the range to R0+.

No. It depends on how the range is defined.

y = x2 is not onto R but can be made onto by changing the range to R0+.

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11y ago
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11y ago

No. It depends on how the range is defined.

y = x2 is not onto R but can be made onto by changing the range to R0+.

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Q: Is every function a onto function?
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it means you are applying the function onto the number.


What type of function maps an input onto itself?

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Is the relation a function?

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No. The function y = x2, where the domain is the real numbers and the codomain is the non-negative reals is onto, but it is not one to one. With the exception of x = 0, it is 2-to-1. Fact, they are completely independent of one another. A function from set X to set Y is onto (or surjective) if everything in Y can be obtained by applying the function by an element of X A function from set X to set Y is one-one (or injective) if no two elements of X are taken to the same element of Y when applied by the function. Notes: 1. A function that is both onto and one-one (injective and surjective) is called bijective. 2. An injective function can be made bijective by changing the set Y to be the image of X under the function. Using this process, any function can be made to be surjective. 3. If the inverse of a surjective function is also a function, then it is bijective.


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In simple words, a one-to-one function is a function such that for every input there is a unique output. An onto function is such that ALL the elements in the out are used, something which is not necessary for a one-to-one function. Draw a set A, which contains 3 elements, a, b, c and d. Draw another set B, containing elements e, f, g and h. Make an arrow from "a" to "d", "b" to "d", then "c" to "e" and "d" to "f". Draw the two sets A and B again. This time make an arrow from "a" to "d", "b" to "d", then "c" to "e" and "d" to "e". The fact that "f" in set B has not been used, DOES NOT makes this function an onto function.


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