I can't seem to Find the domain of the composition f ( g ( x ) .

Hi, right off the bat you can tell x = 0 would cause a problem. You seem to be missing that one. After combining f and g you should check which value of x gives a 0 in the denominator. In this case, you would have to solve for (8/x)+3-2 = 0.

I can't say I am entirely sure of what procedure you followed :p
 
How can we know what you are doing wrong if you do not show your work? Instead of writing this message I could have been giving you excellent help!

What are you computing g of and what can't you compute g of? Hint: You are computing g of x.
What are you computing f of? What can't you compute f of?

So what can't x be?
 
Jomo said:
How can we know what you are doing wrong if you do not show your work? Instead of writing this message I could have been giving you excellent help!

What are you computing g of and what can't you compute g of? Hint: You are computing g of x.
What are you computing f of? What can't you compute f of?

So what can't x be?
Click to expand...
Figured it out finally after 20 tries
 
In order to be in the domain of f(g(x)), x must first be in the domain of g. Then g(x) must be in the domain of f. Here, \(\displaystyle g(x)= \frac{8}{x}+ 3\). Its domain is "all numbers except 0", \(\displaystyle f(x)= \frac{1}{x- 2}\), Its domain is "all numbers except 2". For what x is \(\displaystyle g(x)= \frac{8}{x}+ 3= 2\)?

\(\displaystyle \frac{8}{x}= -1\) so \(\displaystyle x= -8\). The domain of f(g) is "all numbers except 0 and -8". In interval notation that can be written \(\displaystyle (-\infty, -8)\cup(-8, 0)\cup(0, \infty)\).
 
vgamelover123 said:
I forgot to add the infinity sign I mixed up the operations.
Click to expand...
What infinity sign? I'll basically repeat what HallsofIvy said.

In f(g(x)) you need to be able to compute g(x) and then f(g(x)).
You can not compute g(0). Since you need to compute g(x), x can not be 0.
You can not compute f(2). Since you need to compute f(g(x)), g(x) can not be 2. So solve g(x)=2, get x=-8.
In the end, x can not be 0 or -8
 
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