CCSS Honors 8.1 Example 1

Find the function that results from the composition [math](f ∘ g)(x)[/math] if [math]f(x) = \frac{1}{x-3}[/math] and [math]g(x) = \frac{3}{x+5}[/math]. Determine the domains of [math]f(x)[/math], [math]g(x)[/math], and [math](f ∘ g)(x)[/math].

[list=1] [*]To find [math](f ∘ g)(x)[/math], find [math]f(g(x))[/math]. [*]Determine the domain of [math]f(x)[/math]. [*]Determine the domain of [math]g(x)[/math]. [*]Determine the domain of [math](f ∘ g)(x)[/math]. [/list]

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