Hello PeleusAs 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