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\hoffset -0.75truein
%%\voffset -0.1truein
\vsize 9.5truein
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$\matrix{
&~~ f: {\bf R} \rightarrow {\bf R}  ~~~~~~ & g: [0, \infty)  \rightarrow {\bf R}  ~~~~~~ & h: [0, \infty)  \rightarrow  [0, \infty)  \cr
& f(x) = x^2 & g(x) = x^2 & h(x) = x^2 \cr
~& & & \cr
1:1& & & \cr
x_1 \not= x_2   & & & \cr
\hbox{ then }& & & \cr
f(x_1) \not= f(x_2)& & & \cr
~& & & \cr
\hbox{ not }1:1 & & & \cr
\hbox{ there exists }& & & \cr
 x_1 \not= x_2  & & & \cr
\hbox{ such that } & & & \cr
 f(x_1) = f(x_2)& & & \cr
~& & & \cr
~& & & \cr
onto& & & \cr
range = codomain& & & \cr
~& & & \cr
not ~onto& & & \cr
range \not= codomain& & & \cr
~& & & \cr
~& & & \cr
invertible& & & \cr
& & & \cr
& & & \cr
}$

Defn:  Suppose $f: A \rightarrow B$ is 1:1 function where $A$ = domain, $B$ = range, 
then \hfil \break
its inverse function $f^{-1}:B \rightarrow A$ exists and is defined by

\centerline{ $f^{-1}(b) = a$ if and only if $f(a) = b$.}
\end{document}