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March 16th, 2009, 04:20 AM   #1
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Domains and composites.

Hi,

For the function would the domain be any real number except -1, 2 and -11? I'm not sure if I expand the brackets out first or not.

For the functions and are the composites;

f.h =
h.f =

which would then result in both being ? And would the codomain be ?
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March 16th, 2009, 09:59 AM   #2
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Re: Domains and composites.

For the first function, the domain would be
For the second problem:
\mapsto |x|" />
\mapsto x" />
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March 16th, 2009, 03:22 PM   #3
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Re: Domains and composites.

Not -11?

Also, how did you get the first of the composites?
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March 16th, 2009, 06:25 PM   #4
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Re: Domains and composites.

Yes, -11.

For h of f: first you square, then take the (positive) square root. Zero goes to zero, positive x goes to x, negative x goes to -x (which is positive).

For f of h: first you take the square root, then square. Zero goes to zero, positive x goes to x, negative x has no square root and so can't be in the domain.

The codomain for both is all non-negative real numbers.
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March 16th, 2009, 07:41 PM   #5
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Re: Domains and composites.

Aswoods, you mean the range! You don't get to specify the codomain.
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March 17th, 2009, 05:23 AM   #6
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Re: Domains and composites.

Good ol' codomain/range war =]
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