Inverses?

[calculus]

I thought for a function to have an inverse it has to be a one-to-one function or part of the graph has to be a one-to-one function?

In ITUTE Exam 2 Multiple Choice Question 9



Referring to the graph shown, which one of the following statements is false?
A. The relation does not have an inverse.
B. The relation is not a function.
C. The relation is not a one-to-one function.
D. The inverse of the relation is not a function.
E. The inverse of the relation is the relation.

So it says that the graph above has an inverse?
Can someone please explain when a function can/cannot have an inverse?

Thanks!

[fredrick]

i dont see how that has an inverse

[calculus]

Yeah me either :S
But the solutions says that the statement A is false, therefore it does have an inverse??

[kurrymuncher]

I think it is trying to say that the graph does have an inverse, if you restrict its domain.  It means it doesnt have an Inverse FUNCTION, they're different things.

Im just spitballing here, not 100%


Functions can only have inverses when they are one to one functions. "Many to one" functions, like that circle can have inverses if you restrict its domain to become a one to one function

[fredrick]

It would have an inverse if it said it was restricted to [-1,0)

[calculus]

Fair enough, so if the word was "function" rather than "inverse" would A still be false?

[fredrick]

yeh it wouldnt be a function either unless its restricted (ie-for evry x value there is only one unique y-value-this isnt the case from [0,1]

[Mao]

kurrymuncher is correct.

EVERYTHING has an inverse, but only one-to-one relationships have an inverse function

[fredrick]

kurrymuncher is correct.

EVERYTHING has an inverse, but only one-to-one relationships have an inverse function

HAH! wat a retarded question

[unknown id]

The above image is a relation as stated, and not a function. Any relation (regardless of whether it is one-to-one, many-to-one, one-to-many or many-many) can have an inverse but only one-to-one functions can have an inverse that is a function.

[Mao]

The above image is a relation as stated, and not a function. Any relation (regardless of whether it is one-to-one, many-to-one, one-to-many or many-many) can have an inverse but only one-to-one functions can have an inverse that is a function.

not necessarily.
many-to-one relationships can have an inverse function that is one-to-many. try

[kurrymuncher]

kurrymuncher is correct.

EVERYTHING has an inverse, but only one-to-one relationships have an inverse function

HAH! wat a retarded question

yeah, its Itute, they are known to have crazy questions.