Math Is Fun Forum

{7/3}

Member

Registered: 2013-02-11

Posts: 210

2 variable function.

If f(a,b)=f(b,a) and f(a+b,c)=f(a,c)+f(b,c) then what are the solutions for f?

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There are 10 kinds of people in the world,people who understand binary and people who don't.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 2 variable function.

f(a,b)=k*a*b, where k is some constant.

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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.

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: 2 variable function.

How did you derive it?

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There are 10 kinds of people in the world,people who understand binary and people who don't.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 2 variable function.

Well, from the second condition f(a,b)=a*f(1,b), whoch can be proven by induction. Then, we have f(1,b)=f(b,1). And finally f(b,1)=b*f(1,1). So, f(a,b)=a*b*f(1,1) and f(1,1) can be anything we want, so, let's just call it k, where k can be any number. f(a,b)=k*a*b.

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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.

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: 2 variable function.

Thanks.

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There are 10 kinds of people in the world,people who understand binary and people who don't.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 2 variable function.

You're welcome.

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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.