![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step1.JPG\")
The function is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=7ceb59843d6ba546f26f4506214bef60.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=7ceb59843d6ba546f26f4506214bef60.png\")
.
Draw the horizontal line.
\![\"\"](\"/userfiles/23-421-42(2).gif\")
Observe the graph:
\The horizontal line ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c3f40df3b6ee26c4ed5b179d6afd8b20.png\")
passes through the graph 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.