For the Given Functions F and G, Find the Requested $f ( x ) = \frac { 8 x + 5 } { 2 x - 9 } ; g ( x ) = \frac { 4 x } { 2 x - 9 } ; \quad$

question 188

Multiple Choice

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
- $f ( x ) = \frac { 8 x + 5 } { 2 x - 9 } ; g ( x ) = \frac { 4 x } { 2 x - 9 } ; \quad$ Find $f + g$ .

• A) \(( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; ( * , 0 ) \cup ( 0 , \infty )\)
• B) \(( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; \left( \infty , \frac { 9 } { 2 } \right) \cup \left( \frac { 9 } { 2 } , \infty \right)\)
• C) \(( f + g ) ( x ) = \frac { 4 x - 5 } { 2 x - 9 } ; \left( \infty , \frac { 9 } { 2 } \right) \cup \left( \frac { 9 } { 2 } , \infty \right)\)
• D) \(( f + g ) ( x ) = \frac { 12 x + 5 } { 2 x - 9 } ; \left( \infty , - \frac { 5 } { 12 } \right) \cup \left( - \frac { 5 } { 12 } , \infty \right)\)

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Definitions:

Conflict Theory

A sociological perspective that focuses on the inherent divisions of societies based on social inequalities and the way these social divisions give rise to different interests and conflicts.

Nuclear Family

A heterosexual couple with one or more children living in a single household.

Sexual Division

The allocation of tasks, roles, and responsibilities between males and females based on societal norms and expectations, often leading to gender disparities.

Extended Family

A family unit that goes beyond the immediate nuclear family to include other relatives such as grandparents, aunts, uncles, and cousins.