[Note: I really need help on these Domain questions. I've been struggling with this all day]

Question

-Consider the following:

f(x)= 5/x , g(x)= 7/(x+7)

-Find the solutions to the following:

1). (f+g)(x)
2). Domain of (f+g)(x)
[Use interval notation too]
3). (f-g)(x)
4). Domain of (f-g)(x)
[Use interval notation too]
5). (fg)(x)
6). Domain of (fg)(x)
[Use interval notation too]
7). (f/g)(x)
8). Domain of (f/g)(x)
[Use interval notation too]

[Extra Note: You don't have to do interval notation. Just relaying information]

Answer 1

The denominator cannot = 0
For f(x) x cannot = 0
for g(x) x cannot = -7

1) If you add the two fractions together, the denominator will be
x(x+7)

Domain would be from
(-infinity, -7)U(-7,0)U(0,infinity)

Using ( ) because those values aren't included in the domain.

3) you are subtracting so the denominator will be the same as above and your domain will be the same.

Can you finish from here?

Answer 2

the domains include all real numbers except where the denominator is zero.

So, figure the resultant function, and then exclude any places where the denominator is zero.

AND, exclude 0 and -7 because at those values f or g is undefined, so even though some mixture of them might look ok there, f and g have to be evaluated to come up with the result.

So, whaddya get?