Question

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

Answer 1

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

Answer 2

ok

Answer 3

You know what polynomial is, correct?

Answer 4

yes

Answer 5

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?

Answer 6

why is it so? haha

Answer 7

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)

Answer 8

i will do some examples

Answer 9

ok

Answer 10

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....

Answer 11

ok im pretty sure i get it

Answer 12

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

Answer 13

ok

Answer 14

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

Answer 15

okay

Answer 16

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.

Answer 17

okay makes sense

Answer 18

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)

Answer 19

ok

Answer 20

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)

Answer 21

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

polynomial?

Answer 22

are the polynomials?

Answer 23

yes

Answer 24

they are

Answer 25

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

Answer 26

polynomial

Answer 27

yes.

Answer 28

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

Answer 29

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)

Answer 30

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

Answer 31

im following as of right now :)

Answer 32

we know your function is a polynomial (correct?)

So can you give me the domain of your new function, or not yet?

Answer 33

(-∞, +∞)?

Answer 34

yes

Answer 35

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

Answer 36

okay i remember that one

Answer 37

(-∞, +∞)

means from negative infinity to positive infinity

and that is: every single number that there can possible be

Answer 38

i wish you were my math teacher haha

Answer 39

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

Answer 40

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

Answer 41

YOUR ONLY 19!!!!

Answer 42

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

Answer 43

nope i got it :) ty so much

Answer 44

k, yw