Question: Compose two functions and plot

Forgive me for not using the "Maple Math" and "Maple Plot" commands.  I tried, but it says everything that I enter is an invalid expression so I'm just entering it as text...

I define two functions, they plot as expected:


f(x) := sin(x);

g(x) := 2*x;

plot( f(x) );

plot( g(x) );


Now I want to plot the composition:


plot( f(g(x)) ); 


Doesn't work!


Hmm, maybe try using the compose function?


plot(  (f@g)(x) );


Nope, still doesn't work.


But other functions can be composed.  For example,


plot( sin(cos(x)) );

plot(  (sin@cos)(x) );


Those work...

plot(  2*sin(x) );


That works, but


plot (  g(sin(x)) );


does not work even though its identical.  Still,


plot( sin(x*2) );


Does not work!


So my question is given two functions f(x) and g(x), how can I plot the composition?

This has been branched into the following page(s):
Please Wait...