If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain of (f*g)(x)

- anonymous

If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain of (f*g)(x)

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- SolomonZelman

you are multiplying a polynomial times another polynomial.
This will give you a polynomial as well.

- anonymous

ok

- SolomonZelman

You know what polynomial is, correct?

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## More answers

- anonymous

yes

- SolomonZelman

Ok, will you agree with me (if you don't understand why it is so, then ask! but will you agree) that a polynomial is DEFINED for ALL values of x?

- anonymous

why is it so? haha

- SolomonZelman

Ok, i will post a percise and short definition of a polynomial.
"Polynomial" is a function that can have the terms of:
1) Constants (some real numbers)
2) x raised to a power of 1, 2, 3 and on (but the power has to be a whole number)
(and the terms can have any real coefficients)

- SolomonZelman

i will do some examples

- anonymous

ok

- SolomonZelman

polynomials. examples.
y=0
y=-45
y=√3
(or any function y=c where c is a constant)
y=-4x
y=3x+2
y=x-9
(or any function in a form of y=mx or y=mx+b)
y=3x²
y=-5x²+9
y=x²+8
y=x²-7x-7
and so on....

- anonymous

ok im pretty sure i get it

- SolomonZelman

it (a polynomial) terms can be made up and can consist of any terms as long as the terms have x^(whole number)
and other real numbers
ok got the definition

- anonymous

ok

- SolomonZelman

So, really try to think of any polynomial that can have an UNDEFINED X-VALUE.
what I mean by "UNDEFINED X-VALUE" is that if you plug this value for x into the function, then you will get an undefined/indeterminate output for y
in polynomials this "UNDEFINED X-VALUE" never exists

- anonymous

okay

- SolomonZelman

Because if your x's have only whole number powers such as: x\(^1\), x\(^2\), x\(^3\), x\(^4\) then you will get a valid result NO MATTER WHAT you plug in for x.

- anonymous

okay makes sense

- SolomonZelman

now agin, when you multiply two functions where both of these functions are polynomials (i.e. whole number powers of x like 1, 2, 3 and on with or without constants)
then you get after multiplying these two (or any number of) polynomial functions
- you will get - a polynomial function (whole number powers of x like 1, 2, 3 and on with or without constants)

- anonymous

ok

- SolomonZelman

polynomial • polynomial = polynomial
it is good to remember, even if you don't fully comprehend the deepness behind it (you will get it at some time)

- SolomonZelman

now, if your function
f(x)=x²-1
and
g(x)=2x-3
polynomial?

- SolomonZelman

are the polynomials?

- anonymous

yes

- anonymous

they are

- SolomonZelman

so the product of them (when you multiply f • g) will also give you a what?

- anonymous

polynomial

- SolomonZelman

yes.

- SolomonZelman

And again, ANY POLYNOMIAL has a domain of ALL VALUES OF X.
(in interval notation: Domain: (-∞, +∞) )

- SolomonZelman

So will what be the domain of your new function be?
(we know your new function is going to be a polynomial -as we said b4)

- SolomonZelman

if you got questions, you can always ask ....

- anonymous

im following as of right now :)

- SolomonZelman

we know your function is a polynomial (correct?)
So can you give me the domain of your new function, or not yet?

- anonymous

(-∞, +∞)?

- SolomonZelman

yes

- SolomonZelman

the ∞ (or +∞) symbol means infinity
and -∞ means negative infinity --> (same stength but going the negative way)

- anonymous

okay i remember that one

- SolomonZelman

(-∞, +∞)
means from negative infinity to positive infinity
and that is: every single number that there can possible be

- anonymous

i wish you were my math teacher haha

- SolomonZelman

that is the domain of your new polynomail function, or of any polynomial function.....

- SolomonZelman

i am just some 19 yrs old dude....

- anonymous

YOUR ONLY 19!!!!

- SolomonZelman

Math is just something I like:)
In any case, do you have questions regarding this question?

- anonymous

nope i got it :) ty so much

- SolomonZelman

k, yw

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