Consider the Functions Given by F(x)= X + 3 and F^-1(x)=

question 19

Multiple Choice

Consider the functions given by f(x) = x + 3 and f^-1(x) = x - 3.Evaluate f(f^-1(x) ) and f^-1(f(x) ) for the indicated values of x.What can you conclude about the functions
$$\begin{array} { | l | l | l | l | l | } \hline x & - 1 & 0 & 4 & 49 \\\hline f \left( f ^ { - 1 } ( x ) \right) & & & & \\\hline f ^ { - 1 } ( f ( x ) ) & & & & \\\hline\end{array}$$

• A) \[\begin{array} { | l | l | l | l | l | }
• \hline x & - 1 & 0 & 4 & 49 \\
• \hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & - 49 \\
• \hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \\
• \hline
• \end{array}\]We can conclude that, both the functions have the same value for negative variables
• B)\[\begin{array} { | l | l | l | l | l | }
• \hline x & - 1 & 0 & 4 & 49 \\
• \hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \\
• \hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \\
• \hline
• \end{array}\]We can conclude that, both the functions have the same value
• C)\[\begin{array} { | l | l | l | l | l | }
• \hline x & - 1 & 0 & 4 & 49 \\
• \hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \\
• \hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & - 49 \\
• \hline
• \end{array}\]We can conclude that, both the functions have the same value for negative variables.
• D)\[\begin{array} { | l | l | l | l | l | }
• \hline x & - 1 & 0 & 4 & 49 \\
• \hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & 49 \\
• \hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & - 49 \\
• \hline
• \end{array}\]We can conclude that, both the functions are opposite of each other.
• E)\[\begin{array} { | l | l | l | l | l | }
• \hline x & - 1 & 0 & 4 & 49 \\
• \hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & - 49 \\
• \hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & 49 \\
• \hline
• \end{array}\]
• We can conclude that, both the functions are opposite of each other.

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Do Your Best Goal

A type of goal setting where individuals are encouraged to give their best effort without specific, measurable objectives.

Process Theories

Theories in psychology and management that focus on how people perceive and respond to different inputs and how this influences motivation and behavior.

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A preference to avoid negative judgments about the outcome of one’s performance.

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