Composite functions.

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October 16th 2011, 05:01 AM
Fabio010

Composite functions.

Hi people, as you can see i am new in forum.

I just learn today how to solve the domain of composite functions in internet.

I tried to resolve one exercise, and i want to know if i solved it correctly. :/

$f(x) = x^2-3x$
$g(x) = \surd(x+2)$

Maximal Domain of $fog$ and $gof$

ok so lets start with $fog$

domain of $g(x)$ is $x\geq-2$

$f(g(x)) = x+2 - 3\surd(x+2)$

there are no restrictions so the composite domain is $x\geq-2$

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$gof$

Domain of $f(x) = \Re$

$g(f(x)) =$ $\surd(x^2-3x+2)$
the function creates new restrictions so domain is $x\leq1 \cap x\geq2$

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These domain solutions are correct ?
Sorry my english btw.
October 16th 2011, 07:07 AM
emakarov

Re: Composite functions.

Welcome.

Quote:

These domain solutions are correct ?

Yes, except that $\cap$ denotes an intersection of sets, while here we need a union. The answer to the second problem is $\{x\in\mathbb{R}\mid x\le1\}\cup\{x\in\mathbb{R}\mid x\ge2\}$ or something like $(-\infty,1]\cup[2,\infty)$ .
October 16th 2011, 09:44 AM
Fabio010

Re: Composite functions.

Quote:

Originally Posted by emakarov

Welcome.

Yes, except that $\cap$ denotes an intersection of sets, while here we need a union. The answer to the second problem is $\{x\in\mathbb{R}\mid x\le1\}\cup\{x\in\mathbb{R}\mid x\ge2\}$ or something like $(-\infty,1]\cup[2,\infty)$ .

Ok thanks for the help :)
Thanks for showing me the error.