What is the domain of the function?

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What is the domain of the function?

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Answer 1 · 2018-04-08T00:31:56

$x \in (- \infty, \infty)$ $x in (-infty, infty)$
$y \in (\infty, 0) \cup (0, \infty)$ $y in (infty, 0)cup(0, infty)$

Explanation:

Recall that the domain is the set of valid inputs to the function. In this case, it is the set of all pairs $(x, y)$ $(x, y)$ that are valid inputs.

Also recall that, while you cannot take the square root of a negative number, you can take the cube root of a negative number. For example, $\sqrt[3]{- 8} = - 2$ $root(3)(-8) = -2$ . Thus, $\sqrt[3]{x}$ $root(3)(x)$ is valid for any value of $x$ $x$ .

Additionally, $\sqrt[3]{y}$ $root(3)(y)$ is valid for all inputs of $y$ $y$ , but our function $f (x, y) = \frac{\sqrt[3]{x}}{\sqrt[3]{y}}$ $f(x, y) = root(3)(x) / root(3)(y)$ is undefined when $y = 0$ $y = 0$ , due to division by zero.

Thus, our domain is $x \in (- \infty, \infty)$ $x in (-infty, infty)$ , $y \in (- \infty, 0) \cup (0, \infty)$ $y in (-infty,0)cup(0, infty)$ .

Note: This can be more concisely written as $D = {(x, y) \in Z \times Z : y \neq 0}$ $D = {(x, y) in bbZtimesbbZ: y != 0}$ .

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What is the domain of the function?

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