Find the Indicated Function and Write Its Domain in Interval $$s ( x ) = \frac { x - 5 } { x ^ { 2 } - 49 } , t ( x ) = \frac { x - 7 } { 5 - x } , ( s \cdot t ) ( x ) = ?$$

question 53

Multiple Choice

Find the indicated function and write its domain in interval notation.
- $$s ( x ) = \frac { x - 5 } { x ^ { 2 } - 49 } , t ( x ) = \frac { x - 7 } { 5 - x } , ( s \cdot t ) ( x ) = ?$$

• A) \(- \frac { 1 } { x + 7 } ; ( - \infty , - 7 ) \cup ( 7 , \infty )\)
• B) \(\frac { 1 } { 7 - x } ; ( - \infty , - 7 ) \cup ( - 7,5 ) \cup ( 5,7 ) \cup ( 7 , \infty )\)
• C) \(\frac { 1 } { 7 - x } ; ( - \infty , 7 ) \cup ( 7 , \infty )\)
• D) \(- \frac { 1 } { x + 7 } ; ( - \infty , - 7 ) \cup ( - 7,5 ) \cup ( 5,7 ) \cup ( 7 , \infty )\)

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Definitions:

Manufacturing Overhead Costs

Manufacturing Overhead Costs include indirect expenses related to manufacturing, such as utilities, maintenance, and factory management salaries, that are not directly tied to specific units of production.

Activity Rates

These are costs assigned to cost objects based on the activities those objects require, often used in activity-based costing.

Traditional Costing System

A costing methodology that assigns costs to products based on direct costs like materials and labor, and allocates overhead costs based on a predetermined rate.

Activity-Based Costing System

An accounting method that assigns costs to products based on the activities they require for production.