![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step1.JPG\")
The function is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d22db31eba104e9c074fe80fece91309.png\")
.
Horizontal line test:
\A function ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9f8dd602e380fe480d50b678506f1c71.png\")
has an inverse ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d8727a3f2f82e37ee37152d4c4338c36.png\")
if and only if no horizontal line intersects its graph of the function in at most one point.
Graph :
\Graph the function ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d22db31eba104e9c074fe80fece91309.png\")
.
Draw the horizontal line.
\![\"\"](\"/userfiles/23-421-46(1).gif\")
Observe the graph:
\The horizontal line ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=992f15ae33e22d10382e5c207d0a9070.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a4f8c5730f9412f995989427f42e70fc.png\")
passes the graph of the function more than one point.
Therefore the inverse of the function does not exist.
\![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/solution.JPG\")
No, the inverse of the function does not exist.