This math topic focuses on identifying the domain of functions where a linear expression is divided by the square root of a quadratic expression. Specifically, it delves into functions involving the root of quadratics having real roots, and the task involves determining the suitable value sets for which the function is defined without causing mathematical inconsistencies like division by zero or taking the square root of a negative number. The problems aim to enhance understanding of function domains, especially how they are influenced by expression under radicals and denominators.

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Function Domain - Fraction Linear over Root of Quadratic (Real Roots) to Domain Definition Worksheet

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Function Domain - Fraction Linear over Root of Quadratic (Real Roots) to Domain Definition
1
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x+4 over square root of 1x to the power of 2 +5x-14
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -7\text{{ or }}2 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -7 < X < 7\text{{ or }}-2 < X < 2\}
2
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x-2 over square root of 1x to the power of 2 -0x-4
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -2\text{{ or }}2 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -2 < X < 2\text{{ or }}-2 < X < 2\}
3
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x-1 over square root of -1x to the power of 2 -1x-0
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 0\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 \le X \le 0\}
4
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x+2 over square root of 1x to the power of 2 +5x-0
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -5\text{{ or }}0 < X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 < X < 5\text{{ or }}-1 < X < 1\}
5
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x-4 over square root of -1x to the power of 2 -2x-0
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -2 < X < 0\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -2 \le X < 0\}
6
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x+4 over square root of 3x to the power of 2 -6x-9
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -1 < X < 1\text{{ or }}-3 < X < 3\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < -1\text{{ or }}3 < X\}
7
What set describes the domain of this function?
A LaTex expression showing f(x) = -1x-0 over square root of -1x to the power of 2 +7x-12
a A LaTex expression showing \{X \in \mathbb{{R}} \vert 3 < X < 4\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert 3 \le X < 4\}
8
What set describes the domain of this function?
A LaTex expression showing f(x) = 1x+2 over square root of -1x to the power of 2 -8x-15
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 < X < -3\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -5 \le X \le -3\}