I got this problem in my pre-calc algebra class, and I have absolutely no idea how to answer it. The explanation didn't make any sense to me. I assume there's some sort of formula or standard way of approaching this kind of problem, but I haven't been able to find anything in my research. The answer to this specific problem isn't even that important, I just want to know how to solve it.
1 Answer
$\begingroup$Hint for the domain $D$ of $g\circ f$. In order to compose $g$ with $f$ we need to restrict the domain of $f$ to a subset $D$ of the domain of $f$, i.e. $\{3,4,6,7,8,9\}$, such that $f(D)$ is a subset of the domain of $g$, i.e. $\{1,5,7,8,9\}$. For example, since $f(8)=f(3)=4\not \in \{1,5,7,8,9\}$ then $3,8\not \in D$. Moreover $f(4)=9\in \{1,5,7,8,9\}$ and therefore $4\in D$. What is $D$?
Hint for the range of $g\circ f$ i.e. $g(f(D))$. For example, since $4\in D$ then $g(f(4))=g(9)=2\in g(f(D))$. What is $g(f(D))$?
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