Question

f(x)=8/(x+8), g(x)=x+6 find the domain of f of g. I believe the answer is (- infinity, -14) or (-14, +infinity) I'm not sure of my answer though. Could someone please explain?

Answer 1

First you'll want to find the composite function fg(x), remember that this is g(x) then f(x):
\[fg(x) = f(g(x)) = \frac{ 8 }{ g(x)+8 } = \frac{ 8 }{ (x+6)+8 } = \frac{ 8 }{ x +14 }\]
The domain of fg(x) is then the set of values for which fg(x) exists.

Answer 2

yeah that's how I started

Answer 3

Can you see which values the function exists for?