The reason I am trying to 'plot' the function is to visualize the graph and then do composition of one function onto the other and see what it looks like. I don't know how the function would look like. I didn't test it with all the points... I thought the computer was supposed to go through hundreds of points and let ME know what the interval is, and not the other way around.
If I want to plot a function
y = x^2
That's simple enough. I would know the interval. But what if the function is more complicated? So complicated that I cannot figure out the interval... because I do not know the domain of the function. Isn't mathematica supposed to figure that out for me???
Another scenario. Ok, maybe I do figure out the interval, but its wrong, I made an error somewhere. And all mathematica tells me is 'Beep' Your interval is wrong... Shouldn't it 'plot' the graph, tell me, Hey, this is the interval man. Yours is wrong... and that's what I am here for, to correct your math...
I am very sorry if I sound mad, but that's because I am a bit mad with the software (everyone hates a piece of software once in a while because they can't figure out how to work it... lol. Same here... either that, or Mathematica simply refuses to plot ANY graph without the correct interval). Seems that it can do some really complicated math, but sucks at not so complicated (but complicated for humans nevertheless) math.