posted by Dee on .
f(x) = 1/x − 2
g(x) = 1/x − 3
. Determine the domain of the composite function. (Enter your answer using interval notation.)
g compose f
& Find the composite function.
(g compose f)(x) = _____?
g(f) = 1/(f-3) = 1/(1/(x-2)-3) = (2-x)/(3x-7)
So, the domain is all reals except where
3x-7 = 0
x-2=0 (because f(2) is not defined)
f(x) = 3 (because g(3) is not defined)