Hi, there--

The Problem:
Determine f(g(x)) and g(f(x)) for the pair of functions. Also specify the domain for both.

f(x)= 1/x
g(x)= 1/(x-4)

f(g(x)) = f(1/(x-4)) = 1/(1/(x-4)) = x-4

The domain is all real values of x such that x-4 does not equal zero. So x cannot equal 4. In interval notation, the domain is 
(-infinity,4) union (4, infinity). 

Insert appropriate symbols. My software does not write the union sign or infinity (o:

g(f(x)) = g(1/x) = 1/((1/x)-4) = 1/((1/x)-(4x/x)) = 1/((1-4x)/x) = x/(1-4x)

The domain is all real values of x such that 1-4x does not equal zero. So x cannot equal 1/4.
In interval notation, the domain is
(-infinity, 1/4) union *1/4, infinity)

Hope this helps,
Ms.Figgy
math.in.the.vortex@gmail.com