Math Is Fun Forum

siyanor

Member

Registered: 2012-05-09

Posts: 14

domain of a function

hello there,
Lets say we have F(x) = (x-2)÷(x+3)and G(x) = 1÷√(x^2-5x+6) now we have to find domain of each function and domain of f(g(x)), i will not write the calculation but
domain for f(x) = R-{3)
domain for g(x) = (-∞,2)U(3,∞)
domain for f(g(x)) = (-∞,2)U(3,∞)

is the last domain correct?question is also asking to find out if these function are one to one on their domain or not?
i know that f(x) is one to one and already got the answer i also know that g(x) is not one to one , but how we can find inverse of g(x) if its possible ?

Last edited by siyanor (2012-05-11 08:10:59)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: domain of a function

Hi siyanor

Your domain for f(x) is not correct. The finction is defined at 3,but it is not defined at -3.

Also,you don't have to know the inverse of g(x). If two functions are 1 to 1 their composition is also 1 to 1.

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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.

siyanor

Member

Registered: 2012-05-09

Posts: 14

Re: domain of a function

Hi anonimnystefy
Thank you for replying.

you are right for f(x) i have missed the negative sign.
what about he f(g(x)) is it right?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: domain of a function

Yes,g(x) and f(g(x)) are correct.

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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.