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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Definitions:

Intracellular

Located or occurring within a cell or cells.

Body Fluid

Liquids originating from inside the bodies of living organisms, which include substances like blood, urine, and lymph, playing essential roles in their physiology.

Respiratory Acidosis

A medical condition wherein the lungs cannot remove all of the carbon dioxide the body produces, leading to a disturbed acid-base balance.

Arterial Blood Gases

A test that measures the levels of oxygen and carbon dioxide in the arterial blood to assess lung function and how well gases are being exchanged in the body.