what is the domain of (f/g)(x)?
{x|x>_0}
{x|x>2}
{x|x>-2}
{x|xer}<--
f(x)=|x|-1,g(x)=1/x
What is the domain of (fog)(x)
{x|x=/-1}
{x|x=/0} <---
{x|xer}
{x|x=/-1,x=/1}
This is too hard I can't get it.
f/g = (|x|-1)/(1/x) = x(|x|-1)
It would appear that the domain is all real x, but since g(0) is undefined, we have to exclude x=0.
But x≠0 is not one of the choices. Is there a typo somewhere?
(f◦g)(x) = f(g(x))
f(g) = (|g|-1) = (|1/x|-1)
Again, x≠0, so you are correct.
Thanks again Mr.Steve
Am I correct on the first one?
Did you not read what I wrote?
g(0) is not defined, so f/g cannot be defined there.
But x≠0 is not one of the choices, so something is amiss.
Don't worry, I can help you understand how to find the domain of composite functions. Let's break it down step by step.
For the first question, you are given two functions: f(x) = |x| - 1 and g(x) = 1/x. You want to find the domain of the composite function (f/g)(x).
To find the domain of (f/g)(x), you need to consider two things:
1. The domain of the function g(x) itself: Since g(x) involves division by x, it cannot be equal to zero. So the domain of g(x) is all real numbers except x = 0.
2. The values of x that make the function (f/g)(x) undefined: Whenever you have a fraction, the denominator (in this case, g(x)) cannot be equal to zero. So you need to determine if there are any values of x that make g(x) equal to zero.
In this case, g(x) = 1/x, which means it will be equal to zero when x = 0. Therefore, you need to exclude x = 0 from the domain of (f/g)(x). So the domain of (f/g)(x) is all real numbers except x = 0.
Now, let's move on to the second question: finding the domain of the composite function (f∘g)(x), where (f∘g)(x) = f(g(x)).
Again, you have the functions f(x) = |x| - 1 and g(x) = 1/x. To find the domain of (f∘g)(x), you need to consider two things:
1. The values of x for which g(x) is defined: Since g(x) involves division by x, it cannot be equal to zero. So the domain of g(x) is all real numbers except x = 0.
2. The values of x that make the function f(g(x)) undefined: In this case, f(x) = |x| - 1, and we substitute g(x) for x. So the function f(g(x)) will be undefined if g(x) = 0, since |0| - 1 is undefined.
Since g(x) = 0 when x = 0, we need to exclude x = 0 from the domain of (f∘g)(x). So the domain of (f∘g)(x) is all real numbers except x = 0.
I hope this explanation helps you understand how to find the domain of composite functions. If you have any further questions, feel free to ask!