College algebra help! finding F of G!

fuctions f and g are given...
f(x)=5 over x+10 an(x)=8 over x

a.) find fog (f of g) (x) and simplify it
b.) find the domain of fog
c.) find fog(-2).

This is for review for my final exam. I would like to learn how to grasp the concept and answer the problem correctly, so please explain each step. Thanks and will choose best answer!

f(g(x)) is just, what is f(g) when g is x. So go from inside to the outside. In other words, first find g(x) -- and in this case they give it to us as:

g(x) = 8/x

So plug this value into f(x) -- or...

f(8/x) = 5/(x+10)

So plug it in and we get

f(8/x) = 5/(8/x + 10)

f(8/x) = 5x/(8+10x) (after you simplify)

b) Find the domain of fog:

Only thing to worry about here is division by zero, and so...

8+10x ≥ 0

10x ≥ -8

x ≥ -8/10 which is reduced to -4/5 (that's negative 4/5)

So domain is all real except x cannot = -4/5

c) find fog(-2)

So again, plug into fog

f(-2) = 5x/(8+10x)

f(-2) = 5(-2) / (8 + 10(-2))

f(-2) = 5/6

Have a good day!