This math topic focuses on finding the domain of functions that involve a fractional integer over the square root of a quadratic expression, specifically when the quadratic has complex roots. Students are required to identify the valid input values (domain) for functions presented in these forms, ensuring the expressions under the square root remain non-negative to avoid imaginary results. This skill is critical for understanding how to handle functions and expressions involving square roots and complex numbers within the broader context of functions' domain and range.

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

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Function Domain - Fraction Integer over Root of Quadratic (Complex Roots) to Domain Definition
1
A LaTex expression showing f(x) = 3 over square root of 5x to the power of 2 -4x+1
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
2
A LaTex expression showing f(x) = -2 over 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 \}
b A LaTex expression showing \{ \}
3
A LaTex expression showing f(x) = 2 over square root of -1x to the power of 2 +8x-20
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) = 4 over square root of 5x to the power of 2 +8x+5
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert X < 4\}
5
A LaTex expression showing f(x) = -2 over square root of 3x to the power of 2 -4x+10
What set describes the domain of this function?
a A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
b A LaTex expression showing \{ \}
6
A LaTex expression showing f(x) = -3 over square root of -3x to the power of 2 +9x-14
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) = -1 over square root of -1x to the power of 2 +2x-5
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}
8
A LaTex expression showing f(x) = 4 over square root of 2x to the power of 2 -0x+12
What set describes the domain of this function?
a A LaTex expression showing \{ \}
b A LaTex expression showing \{X \in \mathbb{{R}} \vert \}