Let $S$ Be the Set of All Nonzero Real Numbers $g$ From $S$

question 6

Essay

Let $S$ be the set of all nonzero real numbers. Define a function $g$ from $S$ to $S$ by the formula $g ( x ) = \frac { 1 } { x }$ , for all nonzero real numbers $x$ .
(a) Show that $g$ is a one-to-one correspondence from $S$ to $S$ .
(b) Find $g ^ { - 1 }$ .

---

Definitions:

Insomnia

A sleep disorder that is characterized by difficulty falling and/or staying asleep.

Neurons

are nerve cells that are the basic building blocks of the nervous system, responsible for transmitting information throughout the body.

Direct Inner Awareness

The conscious experience or perception of one's own thoughts, feelings, and sensations without the need for external stimuli.

Selective Attention

The cognitive process of focusing on one specific aspect of the environment while ignoring other stimuli.