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

question 224

Multiple Choice

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
- $\begin{array}{l}\begin{array} { c | c } \mathrm { x } & \mathrm { f } ( \mathrm { x } ) \\\hline 2 & 22 \\\hline 10 & - 4 \\\hline 11 & - 12 \\\hline 21 & 20\end{array}\\\\\begin{array} { l | l } \mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \\\hline & \\\hline & \\\hline & \\\hline &\end{array}\end{array}$

• A)\(\begin{array} { c | c }
• \mathrm { x } & \mathrm { f } ( \mathrm { x } ) \\
• \hline 2 & 20 \\
• \hline 10 & 22 \\
• \hline 11 & - 4 \\
• \hline 21 & - 12
• \end{array}\)
• B)\(\text { Not one-to-one }\)
• C)\(\begin{array} { c | c }
• \mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \\
• \hline 22 & 2 \\
• \hline - 4 & 10 \\
• \hline - 12 & 21 \\
• \hline 20 & 11
• \end{array}\)
• D)\(\begin{array} { c | c }
• \mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \\
• \hline 22 & 2 \\
• \hline - 4 & 10 \\
• \hline - 12 & 11 \\
• \hline 20 & 21
• \end{array}\)

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Definitions:

Wage-Price Spiral

A macroeconomic concept describing a situation where rising wages lead to increased prices, which in turn lead to demands for higher wages, thus perpetuating inflation.

Consumer Price Index

A calculation that evaluates the weighted mean prices of a group of consumer items and services, including healthcare, food, and transport, for assessing inflation.

Percent Per Year

A rate or proportion of a quantity expressed as a fraction of 100 per annum.

Inflation

The speed at which the average price of goods and services increases, resulting in a reduction of money's buying power.