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#1 2012-06-27 16:38:35

juantheron
Member
Registered: 2011-10-19
Posts: 312

no. of functions

If A = {1,2,3,4,5,6} and B = {a,b,c,d,e}. Then Total no. of

(1) onto function from A to B

(2) into function from A to B

(3) Constant function from A to B

Explanation Required

Thanks

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#2 2012-06-27 18:43:59

Bob
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Registered: 2010-06-20
Posts: 10,059

Re: no. of functions


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2012-06-27 23:46:38

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: no. of functions

I know it is not the point, but that page is incorrect. A function must be bijective to have an inverse,  not only injective.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2012-06-28 00:11:29

Bob
Administrator
Registered: 2010-06-20
Posts: 10,059

Re: no. of functions

The page talks about restricting the domain for the inverse.

An example would be e^x and ln x.

Have a look at

http://www.mathsisfun.com/sets/function-inverse.html

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2012-06-29 15:47:36

juantheron
Member
Registered: 2011-10-19
Posts: 312

Re: no. of functions

Thanks friends I have got the definition of surjective function and into function

but How can i solve my questions.

please help

Thanks

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#6 2012-06-29 18:31:31

Bob
Administrator
Registered: 2010-06-20
Posts: 10,059

Re: no. of functions

hi juantheron

My diagram shows a possible surjective function and one that isn't because it is not a well defined function.

Every element of B must be mapped onto.

But an element of A cannot map to two elements of B or the mapping is not a function.

So, it seems to me, there must be five connections from a single point to a single point plus one extra connection.

So how many ways can you make the first five and then how many ways can you add on the extra connection?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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