Use the Functions $f ( x ) = \frac { 1 } { 125 } x - 5$

question 21

Multiple Choice

Use the functions $f ( x ) = \frac { 1 } { 125 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$ .

• A) \(( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } + 5 } { 5 }\)
• B) \(( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } - 625 } { 125 }\)
• C) \(( f \circ g ) ^ { - 1 } = \frac { \sqrt [ 3 ] { x + 5 } } { 5 }\)
• D) \(( f \circ g ) ^ { - 1 } = 5 x + 5\)
• E) \(( f \circ g ) ^ { - 1 } = 5 \sqrt [ 3 ] { x + 5 }\)

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Definitions:

Prime Costs

The combined costs of raw materials and direct labor that are directly attributable to the production of goods.

Conversion Costs

The costs incurred to convert raw materials into finished products, including labor and manufacturing overhead expenses.

Factory Overhead

Indirect manufacturing costs not directly linked to the production of goods, such as rent, utilities, and maintenance.

Direct Materials

Raw materials that can be directly traced to the production of a specific product.