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

Level 1

This math topic focuses on determining the domain of a function where the function is given as a fraction with a square root in the numerator and another square root in the denominator. The functions are structured such that the denominator might involve a quadratic expression, potentially with complex roots, requiring the student to assess conditions under which these square roots are defined. The problems presented are multiple-choice questions, each providing sets describing possible function domains for evaluation. This practice is aimed at developing skills to analyze conditions for function validity within the context of real numbers.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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

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Function Domain - Fraction Root of Linear over Root of Quadratic (Complex Roots) to Domain Definition
1
A LaTex expression showing f(x) = \frac{square root of 1x-4}{square root of 2x to the power of 2 +8x+24}
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 4\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert 4 \le X\}
2
A LaTex expression showing f(x) = \frac{square root of -1x+3}{square root of -3x to the power of 2 -10x-19}
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
3
A LaTex expression showing f(x) = \frac{square root of -1x-1}{square root of -5x to the power of 2 -8x-15}
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{ \}
4
A LaTex expression showing f(x) = \frac{square root of 1x-5}{square root of 4x to the power of 2 -10x+18}
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert 5 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le 5\}
5
What set describes the domain of this function?
A LaTex expression showing f(x) = \frac{square root of 1x+3}{square root of 3x to the power of 2 +7x+23}
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -3 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert -3 < X\}
6
A LaTex expression showing f(x) = \frac{square root of -1x+3}{square root of -3x to the power of 2 +7x-21}
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
7
A LaTex expression showing f(x) = \frac{square root of 1x+2}{square root of -4x to the power of 2 -6x-14}
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
8
What set describes the domain of this function?
A LaTex expression showing f(x) = \frac{square root of -1x-3}{square root of 4x to the power of 2 -8x+19}
a A LaTex expression showing \{X \in \mathbb{{R}} \vert -3 \le X\}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X \le -3\}