hello Habi~ This is a good question,even many Chinese also will be confused about "功夫" and "工夫"！When we mention "功夫",most foreigners would think of "Chinese kongfu". 1."工夫" and "功夫" both could mean "time",but "功夫" means "the time you have worked hard on something",for example: (1)He was away for a short while and soon came back. 他出去才一会工夫就回来了。 (2)It took the teacher a few months to make her class under control. 老师费了几个月功夫才把她班上的学生管好。 2.About "功夫" and "工夫",generally they are interchangeable when they both mean "the time/effort/work you have spent/done on somehing": (1)Working requires real effort. 做事须下大功夫/工夫。 (2)One cannot learn English well unless he studies hard. 除非下苦功夫/工夫，否则学不好英语。 3."功夫" means "workmanship; skill; art; ability", in this context you CAN'T replace "功夫" with "工夫"！！！！！！！ (1)If he can complete the task it depends on his skill. 他是否能完成这项任务取决于他的能力/功夫。 (2)Your abilities are not enough. 你的功夫不到家/不够。 I've thought about much time on your question,hope my answer could help you. ^^

“下工夫”是正确的，没有“下功夫”的说法

两者都可以的。工夫，是指时间，下工夫就是在某个东西上花时间。功夫则有两个意思，一个是大家都知道的武术，另一个，和工夫一样。 Both are possible. Work refers to time, make an effort is something on time. Kung Fu there are two meanings, one is we all know martial arts, and the other, and work the same. 用的是goole翻译，以中文为准，哈哈。 Using a goole translated Chinese version shall prevail, ha ha.

下工夫，就是努力做某事。