Choose the One Alternative That Best Completes the Statement or Answers

question 47

Multiple Choice

Choose the one alternative that best completes the statement or answers the question. Graph $f$ as a solid line and $\mathrm { f } ^ { - 1 }$ as a dashed line in the same rectangular coordinate space. Use interval notation to give the domain and range of $f$ and $f ^ { - 1 }$ .
- $$f ( x ) = \sqrt { x - 5 }$$

• A) \(f\) domain \(= ( 0 , \infty )\); range \(= ( 5 , \infty )\) \(f ^ { - 1 }\) domain \(= ( 5 , \infty )\); range \(= ( 0 , \infty )\)
• B) \(f\) domain \(= ( 0 , \infty )\); range \(= ( 5 , \infty )\) \(f ^ { - 1 }\) Has no inverse.
• C) \(f\) domain \(= ( 0 , \infty )\); range \(= ( - 5 , \infty )\) \(f ^ { - 1 }\) domain \(= ( - 5 , \infty )\); range \(= ( 0 , \infty )\)
• D) \(f\) domain \(= ( 0 , \infty )\); range \(= ( 5 , \infty )\) \(f ^ { - 1 }\) domain \(= ( - 5 , \infty )\); range \(= ( 0 , \infty )\)

---

Definitions:

Social World

The domain of human interaction and social relations, encompassing the culture, institutions, and communities of human societies.

Hegel

A German philosopher known for his dialectical method and philosophy of history, which influenced many facets of modern thought.

Kinship

Social bonds and relationships derived from blood ties, marriage, or adoption, which play a crucial role in the social structure and cultural practices of societies.

Substance

In philosophy, the underlying essence or fundamental nature of an entity that determines its properties and existence.