college algebra
posted by Dee .
Let
f(x) = 1/x − 2
and
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/(f3) = 1/(1/(x2)3) = (2x)/(3x7)
So, the domain is all reals except where
3x7 = 0
or
x2=0 (because f(2) is not defined)
or
f(x) = 3 (because g(3) is not defined)