Math Is Fun Forum

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: no. of functions

hi juantheron

Start here:

http://www.mathsisfun.com/sets/injectiv … ctive.html

Bob

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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

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.

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“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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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

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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

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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

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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