Transforming a graph cos(x) to cos(2x-60) in correct order?

[Tangeton]

So I was thinking cos(x) --> cos(2x) --> cos(2x-60) is the correct order, since cos(x) --> cos(x-60) --> cos(2(x-60)) seems to me what would happen if I done the translation of 60 in x and then a stretch of 1/2 parallel to x.

But the book gives me the following order of the transformation: a translation 60 in x and then the stretch, and says its cos(2x-60).

Does the order matter in this case? I am very confused because I've been thought that it does and the book just goes mad with this order.

 

[Tangeton]

So I was thinking cos(x) --> cos(2x) --> cos(2x-60) is the correct order, since cos(x) --> cos(x-60) --> cos(2(x-60)) seems to me what would happen if I done the translation of 60 in x and then a stretch of 1/2 parallel to x.

But the book gives me the order of the translation of 60 in x and THEN the stretch, and says its cos(2x-60).

Does the order matter in this case? Is the book wrong?

 

[Deleted member 4993]

So I was thinking cos(x) --> cos(2x) --> cos(2x-60) is the correct order, since cos(x) --> cos(x-60) --> cos(2(x-60)) seems to me what would happen if I done the translation of 60 in x and then a stretch of 1/2 parallel to x.

But the book gives me the following order of the transformation: a translation 60 in x and then the stretch, and says its cos(2x-60).

Does the order matter in this case? I am very confused because I've been thought that it does and the book just goes mad with this order.

If I were to do this problem, I would follow:

cos(x) → cos(x-30) → cos[2(x-30)] = cos(2x-60)