如果若干个函数的图象经过平移后能够重合，则称这些函数为“互为生成”函数。给出下列函数：
① $f\left(x\right)=\sin x+\cos x$     ②$f\left(x\right)=\sqrt{2}(\sin x+\cos x)$；
③$f\left(x\right)=\sin x$；          ④$f\left(x\right)=\sqrt{2}\sin x+2$其中“互为生成”函数的是(    )

增加：在缺词处加一个漏字符号（∧），并在其下面写出该加的词。

删除：把多余的词用斜线（＼）划掉。

修改：在错的词下划一横线，并在该词下面写出修改后的词。

注意：1）每处错误及其修改均仅限一词。

2）只允许修改10处，多者（从第11处起）不计分。

    I was said that there is a poor countryman, who had nothing but a adult goose. One morning the man went to his goose's nest, and lucky he saw a yellow and glittering egg there.

    He took the eggs home. In his delight, he found that it was an egg of pure gold.

    Every morning the same thing was occurred, and he soon became rich by sell his eggs.

    The countryman became more and more greedy. He wanted get all the gold at once, so he killed the goose. Therefore, when he looked inside, he found nothing in it's body.