很正常的承前省略(重复的成分),都对:
They could do whatever they're asked to do. =
They could do whatever they're asked to.
如果意思清楚的话,可以不重复使用整个动词不定式(和后面的词语),而用 to 代替。
"Are you and Gillian getting married?""We hope to."
"你和吉利恩要结婚吗?""我们希望如此。"
“Let's go for a walk.”“I don't want to.”“咱们去散步吧。”“我不想去。”
I don't dance much now, but I used to a lot. 我现在不怎么跳舞了,可我过去经常跳。
Sorry I shouted at you. I didn't mean to. 对不起,我对你大吼大叫了。我不是故意的。
“Somebody ought to clean up the bathroom.”“I'll ask Jack to.”“该有人把浴室清扫一下了。”“我叫杰克去干吧。”
(以上摘自《牛津英语用法指南》第四版 280.1)
所以,你们英语书上的句子是正确的:
They could do whatever they're asked to.