Given the piecewise function $y = {\sqrt{- x}, - 4 \leq x \leq 0, \sqrt{x}, 0 < x \leq 4$ $y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4$ , how do you find the domain?

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Given the piecewise function $y = {\sqrt{- x}, - 4 \leq x \leq 0, \sqrt{x}, 0 < x \leq 4$ $y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4$ , how do you find the domain?

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Answer 1 · 2015-11-10T11:52:15

The Domain is the set of all values of $x$ $x$ fro which the function is defined; in this case the domain is $[- 4, + 4]$ $[-4,+4]$

Explanation:

Given
$XX y = {(\sqrt{- x} for - 4 \leq x \leq 0), (\sqrt{x} for 0 < x \leq 4)}$ $color(white)("XX")y = {(sqrt(-x)" for "-4 <= x <=0), (sqrt(x)" for "0 < x <=4)}$

The first element of this set definition defines the function for all values of $x \in [- 4, 0]$ $x in [-4,0]$

The second element in this set definition defines the function for all values of $x \in (0, + 4]$ $x in (0,+4]$

Togheter they define the function for all values of $x \in [- 4, + 4]$ $x in [-4,+4]$

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Given the piecewise function $y = {\sqrt{- x}, - 4 \leq x \leq 0, \sqrt{x}, 0 < x \leq 4$ $y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4$ , how do you find the domain?

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Given the piecewise function y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4y={√−x,−4≤x≤0,√x,0<x≤4y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4, how do you find the domain?

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Given the piecewise function $y = {\sqrt{- x}, - 4 \leq x \leq 0, \sqrt{x}, 0 < x \leq 4$ $y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4$ , how do you find the domain?