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?

Is your problem the composition of two functions? or, moreover, finding the domains and ranges? — Mikasa, Nov 21 '13 at 07:00

score 3 · Answer 1 · answered Nov 21 '13 at 07:52

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}

answered Nov 21 '13 at 07:52

acer

5,293

Apart from discontinuities, you can try to find any other restrictions on the domain. Eg, compare the unretricted result x=x from solve({evalc(Im((x+1)/(x-1)))=0},x); with the restricted domain (union) {1 < x}, {0 <= x, x < 1} returned by solve({evalc(Im((sqrt(x)+1)/(x-1)))=0},x); – acer Nov 21 '13 at 08:01
May I ask your point of view doing this by Maple? Thanks acer. – Mikasa Nov 22 '13 at 09:15

score 1 · Answer 2 · edited Nov 21 '13 at 07:03

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.

edited Nov 21 '13 at 07:03

Mikasa

67,374

answered Nov 21 '13 at 07:01

Mhenni Benghorbal

47,431

@B.S.: Thanks for the edit. I really appreciate it. – Mhenni Benghorbal Nov 21 '13 at 07:04
$\ddot\smile{}{}$ – Mikasa Nov 21 '13 at 07:05

score 1 · Answer 3 · answered Nov 21 '13 at 07:34

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]

Domain of Composite Functions by using Maple

3 Answers3