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}

\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.

Determine Whether the Function Has an Inverse Function f−1(x)=x+4f ^ { - 1 } ( x ) = \sqrt { x } + 4f−1(x)=x​+4

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Determine Whether the Function Has an Inverse Function $f ^ { - 1 } ( x ) = \sqrt { x } + 4$

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