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- Thread starter Alem2000
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You can't find the domain of a function. It is usually given, implicitly or otherwise. Let h(x) = f(g(x)). What is the domain of h? What is the range? It should be obvious from the expression.Alem2000 said:

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arildno

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These types of exercises should usually be interpreted as "what is the maximal domain this function can have?"

In the given exercise, we have:

[tex]f(x)=\sqrt{x-2},g(x)=2-\sqrt{x}[/tex]

Hence, for f(g(x)), we need g(x)>=2

This means: [tex]2-\sqrt{x}\geq{2}\to\sqrt{x}<=0[/tex]

Hence, only a single x-value is eligible as the domain of f(g(x)), namely x=0,

so that is the (maximal) domain.

In the given exercise, we have:

[tex]f(x)=\sqrt{x-2},g(x)=2-\sqrt{x}[/tex]

Hence, for f(g(x)), we need g(x)>=2

This means: [tex]2-\sqrt{x}\geq{2}\to\sqrt{x}<=0[/tex]

Hence, only a single x-value is eligible as the domain of f(g(x)), namely x=0,

so that is the (maximal) domain.

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But this depends on whether f is defined on the reals. If the range of f is a subset of the complex numbers, then the 'maximal domain' is just the domain. This brings me back to my previous post.arildno said:[tex]f(x)=\sqrt{x-2},g(x)=2-\sqrt{x}[/tex]

Hence, for f(g(x)), we need g(x)>=2

...

- #5

arildno

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So, I stand by my answer as most probably correct

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