Domain of Composite Functions by using Maple

Question

I have two functions $f(x)=\frac{(x+1)}{(x-1)}$ and $g(x)=\frac{(x-1)}{(x+1)}$. I need to confirm by using maple that $D_{fog}=R-\{-1\}$ and $D_{gof}=R-\{0,1\}$. When I try f@g and g@f syntax im CompositionPlot command on Maple prompt, I get graphs which does not show the discontinuities. How to handle such situations in Maple?

Answer 1

You need to create a function first. So, in your case, we have in maple language

[> f := x -> (x+1)/(x-1); 
   g := x-> (x-1)/(x+1);
   h := (g@f)(x);

This will give you the composition of the two functions.

Answer 2

You might consult Maple to examine the functions $g\circ f(x)$ and $f\circ g(x)$ and finding their asymptotes. I mean vertical an horizontal ones. The data which is achieved can help us to have a good perspective of domains and also ranges. Here are the needed codes:

[> f := x-> (x+1)/(x-1): 
   g := x-> (x-1)/(x+1):
   h := x-> simplify((g@f)(x),symbolic);

                                     h(x)=1/x
[> with(Student[Calculus1]):
   Asymptotes(h(x), x);
                                  [y = 0, x = 0]

Answer 3

f:=x->(x+1)/(x-1):
g:=x->(x-1)/(x+1):

discont((f@g)(x),x);
                          {-1}

discont((g@f)(x),x);
                         {0, 1}