Determine the Domain and Range of the Inverse Function $f ^ { - 1 }$

question 74

Multiple Choice

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 8 | - 3$ , where $x > - 8$

• A) Domain: \([ - 8 , \infty )\); Range: \([ - 3 , \infty )\)
• B) Domain: \(( - \infty , - 3 ]\); Range: \([ - 8 , \infty )\)
• C) Domain: \([ - 8 , - 3 ]\); Range: \([ - 8 , \infty )\)
• D) Domain: \(( - \infty , - 8 ]\); Range: \([ 3 , \infty )\)
• E) Domain: \(( - \infty , \infty )\); Range: \(( - \infty , \infty )\)

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Definitions:

Ligases

Enzymes that catalyze the joining of two molecules by forming a new chemical bond, often requiring the expenditure of energy derived from ATP.

Polymerase

An enzyme that synthesizes long chains or polymers of nucleic acids.

Thermus Aquaticus

A species of bacterium that can tolerate high temperatures, from which Taq polymerase, an enzyme used in PCR, is derived.

Hydrothermal Vents

Deep-sea features where mineral-rich water is released from the Earth's crust, supporting unique ecosystems independent of sunlight.