Domain of composite function

Hello Peleus Quote:

Originally Posted by

**Peleus** Hi all,

First things first, what I've seen as the answer for these is described as follows.

I'm not sure what is meant by the second section though, g(x) in Dom f?

For instance

So the dom for f(x) is [-2, 2]

the dom for g(x) is (0, inf]

How does it work fitting into this formula?

So Dom(fog) = 0 < x < 2 ???

I know this is incorrect, but this is how my logic of applying the formula works.

Anyone who can point out my mistakes or explain it in english a bit better would be appreciated.

As I'm sure you know, when we 'feed' the value through the composite function , is first 'fed into' , and then the output of (which is represented by ) is then used as the input to the function . To ensure a valid input into , then, we must make sure that the output lies in the domain of . That is what is meant by .

As far as the example you quote is concerned, , any value of in the domain will produce an output from , but not every output can then be used as an input to : only those outputs that are themselves in .

So you need to ask yourself the question: What values of can I use as inputs for that will produce outputs in the range ? The answer will be given by the solutions to the equations and .

Raising to the power of both sides of each equation we get:

and

There's the domain of , then:

Grandad