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Why does the function x^2 not have an inverse?

^Basically what the title says.
Original post by sabahshahed294
^Basically what the title says.


f(x) = x^2 is not a one-to-one function, meaning for each f(x) value there are more than one possible x value.
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Avatar for Naruke
Naruke
11
Original post by sabahshahed294
^Basically what the title says.


only bijective functions have inverses. However, it is possible to turn functions that are not bijective into bijective functions by tweaking the domain.
Original post by SherlockHolmes
f(x) = x^2 is not a one-to-one function, meaning for each f(x) value there are more than one possible x value.


So, only functions which are one-to-one functions have inverses?

Original post by Naruke
only bijective functions have inverses. However, it is possible to turn functions that are not bijective into bijective functions by tweaking the domain.


If you don't mind but can you explain how? :smile:
(edited 7 years ago)
Original post by sabahshahed294
So, only functions which are not one-to-one functions have inverses?



If you don't mind but can you explain how? :smile:


No. Only one-to-one functions have inverses.
Original post by SherlockHolmes
No. Only one-to-one functions have inverses.


Yeah, edited my post. Sorry I misread your post at first. :tongue:
Reply 6
Avatar for ntada99
ntada99
7
Original post by sabahshahed294
^Basically what the title says.


Only one-to-one functions have inverses, as the inverse of a many-to-one function would be one-to-many, which isn't a function.

x^2 is a many-to-one function because two values of x give the same value
e.g. both 3 and -3 map to 9

Hope this helps:smile:
You can have f(x) = x^2 to be a one-to-one function if you restrict the domain as mentioned.

For example: f(x) = x^2, x ≥ 0 or f(x) = x^2, x ≤ 0. This means you'll half of the U shaped graph so it now becomes a one-to-one function
Original post by sabahshahed294
So, only functions which are one-to-one functions have inverses?


So yes this is now correct.
Original post by sabahshahed294
So, only functions which are one-to-one functions have inverses?



If you don't mind but can you explain how? :smile:


basically the idea is the inverse of y=x^2 would have to be x=+/-sqrt(y) (which is multivalued so not a function), so if we restrict ourselves to the right-hand side of the original parabola (where x>=0), we get x=sqrt(y), and if we instead look just at the left-hand side (where x<0), we get x=-sqrt(y).
Original post by ntada99
Only one-to-one functions have inverses, as the inverse of a many-to-one function would be one-to-many, which isn't a function.

x^2 is a many-to-one function because two values of x give the same value
e.g. both 3 and -3 map to 9

Hope this helps:smile:


Yeah, got the idea. Thank you. :smile:

Original post by ManLike007
You can have f(x) = x^2 to be a one-to-one function if you restrict the domain as mentioned.

For example: f(x) = x^2, x ≥ 0 or f(x) = x^2, x ≤ 0. This means you'll half of the U shaped graph so it now becomes a one-to-one function


Understood. Thanks :smile:

Original post by SherlockHolmes
So yes this is now correct.


Thank you

Original post by HapaxOromenon3
basically the idea is the inverse of y=x^2 would have to be x=+/-sqrt(y) (which is multivalued so not a function), so if we restrict ourselves to the right-hand side of the original parabola (where x>=0), we get x=sqrt(y), and if we instead look just at the left-hand side (where x<0), we get x=-sqrt(y).


Thank you, got it now! :smile:

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