¿Could the domain of a compound function be obtained in the same way that non-compound functions?(adsbygoogle = window.adsbygoogle || []).push({});

I think the answer is not, like in this example:

f(x)=1/x²

g(x)=√(2x-6)

f(g(x))=1/(√(2x-6))²

Recently Hurkyl explained me that (a^b)^c is not always equal to a^bc, although, I've proved this step with Derive and it seems to be fine.

f(g(x))=1/(2x-6)

Back to the matter, the domain of the function H(x)=1/(2x-6) isR- {3}

But the domain of f(g(x))=1/(2x-6) is (3,∞)

So, Am I right in the fact that a compound function can have a different domain than the "same function" which isn't the product of a composition of functions?

As always, excuse me if my english isn't very clear.

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# Homework Help: Another question about the domain in a compound function

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