Question

If the domain of each of the functions f(x) and g(x) is all real numbers, will the domain of (f/g)(x) also be all real numbers? Why or why not?

Answer 1

hi, can you help me?

Answer 2

What are YOUR thoughts on this?

Suppose that g(x) were x-2. Does this make it any easier for you to answer this question?

Answer 3

No, I am really confused on how (f/g)(x) could even be a function

Answer 4

noo he left :c

Answer 5

nvm

Answer 6

I did not leave. OpenStudy's connection is interrupted every now and then and nothing goes through. I was typing a response to you when this happened.

Answer 7

Given two functions f and g, you can find their sum, difference, product, quotient, composition, and so on.

Answer 8

ok...

Answer 9

(f/g)(x) is the QUOTIENT of functions f and g: f divided by g.

Answer 10

ok...

Answer 11

Take a look at (f/g)(x) when g(x)=x-2:

It is

f(x)
------
x-2

What is the domain of this new function?

Answer 12

What does "domain" mean to you?

Answer 13

x-2

Answer 14

domain means the x values

Answer 15

it means more than that, actually. Domains are written either as (1) the set of all PERMITTED x values or (2) the values at which the function is NOT defined.

x-2 is not a domain; it is an algebraic expression.

What x value can

f(x)
----
x-2

not be evaluated at? and why?

Answer 16

x has to be greater than 3 right? @mathmale

Answer 17

Actually, x can NOT be = to 2. x can take on any other value. so "x has to be greater than 3" is too restrictive.

What is the domain of

f(x)
--------
x-2

When the domain of f(x) is "the set of all real numbers?"

Answer 18

Oh ok I get it now! @mathmale