# why do inverse functions only exist for one to one functions

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rxrx2004

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#1

like y=x^2 is a many to one function, but it has an inverse as it can be reflected in the line y=x?

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mqb2766

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#2

(Original post by

like y=x^2 is a many to one function, but it has an inverse as it can be reflected in the line y=x?

**rxrx2004**)like y=x^2 is a many to one function, but it has an inverse as it can be reflected in the line y=x?

Last edited by mqb2766; 3 months ago

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Pangol

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**rxrx2004**)

like y=x^2 is a many to one function, but it has an inverse as it can be reflected in the line y=x?

^{2}, then, for example, f(1) = 1 and f(-1) = 1. But what would be f

^{-1}(1)?

Last edited by Pangol; 3 months ago

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rxrx2004

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(Original post by

Part of the definition of a function is that it has to be well-defined, in the sense that if you are given a value to plug in, you get one value out. In your example (but using functional notation), if f(x) = x

**Pangol**)Part of the definition of a function is that it has to be well-defined, in the sense that if you are given a value to plug in, you get one value out. In your example (but using functional notation), if f(x) = x

^{2}, then, for example, f(1) = 1 and f(-1) = 1. But what would be f^{-1}(1)?
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mqb2766

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#5

(Original post by

but why

**rxrx2004**)but why

Is a pretty good overview. A function (forwards or inverse, they're both functions) should evaluate to a single value. The inverse function is defined as per the previous post.

This is why

sqrt(2^2) = 2

i.e. its defined to be the positive root (single valued).

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RDKGames

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(Original post by

1 or -1

**rxrx2004**)1 or -1

You cannot say that because that’s two outputs … so is not an inverse function …

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Pangol

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(Original post by

1 or -1

**rxrx2004**)1 or -1

^{-1}were a function, you would be able to tell me the

*one*value of f

^{-1}(1). But there isn't a single value, so it is not a function.

Last edited by Pangol; 3 months ago

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rxrx2004

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(Original post by

https://learn.lboro.ac.uk/archive/ol..._functions.pdf

Is a pretty good overview. A function (forwards or inverse, they're both functions) should evaluate to a single value. The inverse function is defined as per the previous post.

This is why

sqrt(2^2) = 2

i.e. its defined to be the positive root (single valued).

**mqb2766**)https://learn.lboro.ac.uk/archive/ol..._functions.pdf

Is a pretty good overview. A function (forwards or inverse, they're both functions) should evaluate to a single value. The inverse function is defined as per the previous post.

This is why

sqrt(2^2) = 2

i.e. its defined to be the positive root (single valued).

(Original post by

Functions only have a single output.

You cannot say that because that’s two outputs … so is not an inverse function …

**RDKGames**)Functions only have a single output.

You cannot say that because that’s two outputs … so is not an inverse function …

(Original post by

Well that's the problem. If f

**Pangol**)Well that's the problem. If f

^{-1}were a function, you would be able to tell me the*one*value of f^{-1}(1). But there isn't a single value, so it is not a function.
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#9

**rxrx2004**)

like y=x^2 is a many to one function, but it has an inverse as it can be reflected in the line y=x?

Last edited by rxrx2004; 3 months ago

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mqb2766

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(Original post by

wait so y=x^2 isnt a function then?

**rxrx2004**)wait so y=x^2 isnt a function then?

its inverse however is only defined on the functions domain x>=0

Last edited by mqb2766; 3 months ago

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Pangol

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#11

(Original post by

wait so y=x^2 isnt a function then?

**rxrx2004**)wait so y=x^2 isnt a function then?

^{2}. For any value of x, there is only one value of x

^{2}.

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#12

(Original post by

You don't run into the problem with f(x) = x

**Pangol**)You don't run into the problem with f(x) = x

^{2}. For any value of x, there is only one value of x^{2}.
(Original post by

Yes it is, it evaluates to a single value.

its inverse however is only defined on the functions domain x>=0

**mqb2766**)Yes it is, it evaluates to a single value.

its inverse however is only defined on the functions domain x>=0

so y=root x isnt a function..i think i get it now

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#15

(Original post by

Well it is, because

**Pangol**)Well it is, because

**For example, the square root of 9 is 3, it's just the case that the square of negative 3 is also 9.***the definition of square root is to take the positive root.*
(Original post by

It is a function, as its single valued. It returns positive values (and 0).

**mqb2766**)It is a function, as its single valued. It returns positive values (and 0).

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#16

(Original post by

but-but i always thought that you add a plus-minus sign at the front of a square root

but if you reflect the graph of y=x^2 in the line y=x you'd get a graph for which it returns two values?

**rxrx2004**)but-but i always thought that you add a plus-minus sign at the front of a square root

but if you reflect the graph of y=x^2 in the line y=x you'd get a graph for which it returns two values?

You have to multiply it by -1 to get the corresponding negative root as it is defined to return the (single valued) positive value.

If it returned both values (it doesn't) there would be no need to write the +/-.

Last edited by mqb2766; 3 months ago

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