1. ## 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. :/

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

Maximal Domain of $\displaystyle fog$ and $\displaystyle gof$

ok so lets start with $\displaystyle fog$

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

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

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

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$\displaystyle gof$

Domain of $\displaystyle f(x) = \Re$

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

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These domain solutions are correct ?
Sorry my english btw.

2. ## Re: Composite functions.

Welcome.

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

3. ## Re: Composite functions.

Originally Posted by emakarov
Welcome.

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

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