composite functions

[methodsboy]

hi
For f (gx))  ---> the domain is the domain of g(x))
what would be the range of f (g(x)) ?
im worried that this type of question may come up in tommorrows exam

[ReVeL]

If you have the domain, can't you find the range by sketching etc.?

[shinny]

Just work it out as you normally would (i.e. graphing in most cases) given the restrictions imposed by the domain of I don't think there's any shortcut.

[methodsboy]

yes i know that is one way of doing it
but whats another way?

[shinny]

There usually isn't one from what I know. Depends on what the composite function is and what you know already. If the composite function is something like i.e. a linear function, and you know its range already, and you want the range of , then you could just use knowledge of transformations to adjust the range accordingly. But this obviously doesn't work if you get something whack like for example. In those cases, just find it out as you normally would. Like I said, I don't think there's any shortcut so stop trying to find one <_<