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HSF.BF.A.1.b Tutor Intake — Combining Functions with Arithmetic Operations

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Grade 9·12 problems·~12 min·Common Core Math - HS Functions·standard·hsf-bf-a-1b

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Concepts

Let $f(x) = \sqrt{x}$ (defined for $x \geq 0$ ) and $g(x) = \dfrac{1}{x - 3}$
(defined for $x \neq 3$ ). What is the domain of $(f + g)(x)$ ?

All real numbers

$x \geq 0$ or $x \neq 3$ (union of individual domains)

$[0,\, 3) \cup (3,\, \infty)$

$x > 3$