Have you tried assigning the img function to a variable, and passing that to the anchor function? Something along the lines of:
<?php $img = img('../application/images/Home_up.png'); ?>
<li><?php echo anchor('home', $img); ?></li>
Be sure you have the HTML and URL helpers loaded.
Edit @Dolph and everyone else: This is now TESTED. It WORKS as of 1.7.2.
Perhaps instead of downvoting me, you could have tested it yourself and proved me wrong. Also, I don't see anywhere in his original post anything like the above code. He passed the img function output right into the anchor function - which does not always work. Two functions that spring to mind that wont let you do this are isset and empty. There are many more.