How do I find the domain for FOG

[neridao]

I can't for the life of me figure out how to find the domain of FOG but I can find (FOG)(X) so I got 5(x-2)/2x-3 I just need to find the domain of that.

 

[Harry_the_cat]

What can't x be? The domain is basically everything else.

 

[Dr.Peterson]

I can't for the life of me figure out how to find the domain of FOG but I can find (FOG)(X) so I got 5(x-2)/2x-3 I just need to find the domain of that.

I have two comments:

First, do you mean (f o g)(x) = 5(x-2)/(2x-3)? Parentheses are important, and I suspect you've omitted them.

Second, when you find the domain of a composite function, if you have simplified anything, the final form may not reveal the domain, which can be hidden by cancellation. You need to state the actual problem, identifying f and g; the domain of f o g must not include anything that is not in the domain of g.

But Harry has correctly stated what you need to do, both in function g and in the (unsimplified version of) the composite: Look for what can prevent you from evaluating the function, and "don't do that".