If the Following Defines a One-To-One Function, Find Its Inverse

question 114

Multiple Choice

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
- $$\begin{array}{l}\begin{array} { c | c } x & f ( x ) \\\hline 2 & 24 \\\hline 9 & - 4 \\\hline 13 & - 4 \\\hline 17 & 18\end{array}\\\\\begin{array} { l | l } \mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \\\hline & \\\hline & \\\hline & \\\hline &\end{array}\end{array}$$

• A)\(\begin{array} { c | c }
• \mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \\
• \hline 24 & 2 \\
• \hline - 4 & 9 \\
• \hline - 4 & 13 \\
• \hline 18 & 17
• \end{array}\)
• B)\(\begin{array} { c | c }
• \mathrm { x } & \mathrm { f } ( \mathrm { x } ) \\
• \hline 2 & 18 \\
• \hline 9 & 24 \\
• \hline 13 & - 4 \\
• \hline 17 & - 4
• \end{array}\)
• C)\(\text { Not one-to-one }\)
• D)\(\begin{array} { c | c }
• \mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \\
• \hline 24 & 2 \\
• \hline - 4 & 9 \\
• \hline - 4 & 17 \\
• \hline 18 & 13
• \end{array}\)

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Definitions:

Barriers to Entry

These are obstacles that prevent new competitors from easily entering an industry or area of business.

Oligopoly

A market structure characterized by a small number of firms that have significant control over market prices and competition.

Interdependence

The mutual reliance among businesses, individuals, industries, or economies, where the actions of one participant affect the outcomes of another.

Rivals

Competitors within the same industry or market that vie for the same customer base.