The Function F Is One-To-One $$f ( x ) = \frac { 1 } { 4 x + 3 }$$

question 122

Multiple Choice

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder
notation.
- $$f ( x ) = \frac { 1 } { 4 x + 3 }$$

• A) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq - 3 \}\);
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 3 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 3 } { 4 } \right\} \right.\]
• B) \(f ( x ) : D = \left\{ x \mid x z - \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq 0 \}\);
• \[f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 0 \} , R = \left\{ y \mid y \neq - \frac { 3 } { 4 } \right\}\]
• C) \(f ( x )\) : D is all real numbers, \(R\) is all real numbers;
• \(\mathrm { f } ^ { - 1 } ( \mathrm { x } )\) : \(\mathrm { D }\) is all real numbers, \(\mathrm { R }\) is all real numbers
• D) \(f ( x ) : D = \left\{ x \mid x \neq \frac { 1 } { 4 } \right\} , R = \left\{ y \mid y \neq \frac { 1 } { 3 } \right\}\)
• \[\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 3 } \right\} , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 1 } { 4 } \right\}\]

Explore the role of ingroup bias and outgroup homogeneity in fostering prejudice.

Examine the influences of social identities and social inequalities on prejudice.

Recognize the prevalence and implications of gender and sexual orientation prejudices.

Understand the consequences of societal biases on minority and marginalized groups.

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Definitions:

Laws of Supply

Economic principles stating that as the price of a good or service increases, the quantity supplied of that good or service rises, and vice versa.

Developed, Democratic Countries

Nations characterized by advanced economic development, democratic governance, and high levels of social welfare.

Market Economies

Economic systems where supply and demand from consumers drive the production, allocation, and distribution of resources.

Privatisation

The selling of state‐owned enterprises into private ownership.