Determine Algebraically Whether the Following Function Is One-To-One $f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$

question 37

Multiple Choice

Determine algebraically whether the following function is one-to-one.
$f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$ , where $x > 0$

• A)
• \[\begin{aligned}
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \\
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \\
• \frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \\
• \frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { not one-to- } \\
• 30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \\
• 5 a ^ { 2 } & = 5 b ^ { 2 } \\
• a ^ { 2 } & = b ^ { 2 } \\
• \pm a & = \pm b
• \end{aligned}\]
• B)
• \[\begin{aligned}
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \\
• \frac { 5 } { 3 + 6 } & = \frac { 5 } { 3 + 6 } ; \text { one-to- } \\
• \frac { 5 } { 6 } & = \frac { 3 } { 6 } \\
• a & = b
• \end{aligned}\]
• C)
• \[\begin{aligned}
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \\
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } ; \text { one-to-one } \\
• \frac { 5 } { 3 } & = \frac { 5 } { 3 } \\
• a & = b
• \end{aligned}\]
• D)
• \[\begin{aligned}
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \\
• \frac { 5 a ^ { 2 } } { 9 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 9 b ^ { 2 } } \\
• \frac { 5 a } { 9 } & = \frac { 5 b } { 9 } \\
• 5 a & = 5 b \\
• a & = \text { one-to-one }
• \end{aligned}\]
• E)
• \[\begin{aligned}
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \\
• \frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \\
• \frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \\
• \frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { one-to-one } \\
• 30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \\
• 5 a ^ { 2 } & = 5 b ^ { 2 } \\
• a ^ { 2 } & = b ^ { 2 } \\
• a & = b
• \end{aligned}\]

Identify and evaluate the physical and social constructed differences between men and women.

Comprehend the influence of cultural norms and parental attitudes on gender roles and their consequences.

Differentiate between various feminist theories and their perspectives on gender issues.

Explain how socialization agents (parents, peers, etc.) influence gender identity and roles.

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Definitions:

Guilt Proneness

The predisposition of an individual to feel guilty for wrongdoing, even when such guilt may not be warranted.

Collective Guilt

The emotion felt when individuals perceive their group as responsible for wrongful actions, even if they as individuals did not participate in such actions.

Ingroup Bias

The tendency to favor one's own group over other groups.

Empathy Gap

The difficulty of understanding or predicting one's own and others' feelings, preferences, or behaviors when in a different emotional or physical state.