@mathmale Hi! Can you tell me how to find if a relation is a function? And whether it's inverse is one too?

Question

@mathmale  Hi! Can you tell me how to find if a relation is a function? And whether it's inverse is one too?

jdoe0001 · Answer

keep in mind that only one-to-one functions have inverse functions $\bf 
\begin{array}{llll}
\textit{unique "x" for every "y"}\
\textit{one to one function}
\end{array}
\begin{array}{llll}
x&y\
\hline\
a&b\
c&d\
e&f\
g&h\
i&j
\end{array}\qquad

\begin{array}{llll}
\textit{if "x" has repeats}\
\textit{is not a function}
\end{array}
\begin{array}{llll}
x&y\
\hline\
a&b\
{\color{red}{ c}}&d\
d&f\
g&h\
{\color{red}{ c}}&j
\end{array}\ \quad \

\begin{array}{llll}
\textit{if "y" has repeats, is NOT }\
\textit{one to one function}
\end{array}
\begin{array}{llll}
x&y\
\hline\
a&{\color{red}{ b}}\
c&d\
e&f\
g&{\color{red}{ b}}\
i&j
\end{array}$