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

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.