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 $g ^ { - 1 }$ .

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