![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step1.JPG\")
The function is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=40f7678273ab5d7e9625b25636a04532.png\")
.
Horizontal line test:
\A function ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=7638897a5bb9204998d7996637c7b50a.png\")
has an inverse ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=95580a6e5e13d71955ddcf26a364f83b.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=40f7678273ab5d7e9625b25636a04532.png\")
.
Draw the horizontal line.
\![\"\"](\"/userfiles/23-421-43.gif\")
Observe the graph:
\No horizontal line can be drawn more than one point.
\Therefore the inverse of the function exists.
\![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/solution.JPG\")
Yes, the inverse of the function exists.