Warning: include_once(Mage/Core/functions): failed to open stream: No such file or directory in /var/www/html/magento/app/Mage.php on line 50

Warning: include_once(): Failed opening 'Mage/Core/functions' for inclusion (include_path='/var/www/html/magento/app/code/local:/var/www/html/magento/app/code/community:/var/www/html/magento/app/code/core:/var/www/html/magento/lib:.:/usr/share/pear:/usr/share/php') in /var/www/html/magento/app/Mage.php on line 50

Fatal error: Call to undefined function is_dir_writeable() in /var/www/html/magento/app/code/core/Mage/Core/Model/Config/Options.php on line 220